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Publications

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  • Synopsis: 1 edited book, 1 special issue of journal, 9 contributions to books, 64 papers in refereed research journals, 29 papers in refereed conference proceedings, 8 in non-refereed proceedings, 3 papers submitted, 1 paper in preparation (not listed), 3 featured book reviews, 10 additional book reviews (not listed), 2 research monographs, 8 technical reports, 2 theses, and 28 conference abstracts (not listed).


  • The Ph.D. Dissertations and Masters Theses of my students are under item 10 below.
  • 1  Edited Books

    1. C. W. Curtis, A. Dzhamay, W. A. Hereman, and B. Prinari, Eds., Preface: Nonlinear Wave Equations: Analytic and Computational Techniques, American Mathematical Society (AMS) Contemporary Mathematics Series, vol. 635, AMS, Providence, RI (2015).

    2  Special Issues of Journals

    1. W. Hereman, Editor, Special Issue on Continuous and Discrete Integrable Systems with Applications, Applicable Analysis, vol. 89 (4), pp. 429-644 (2010).

    3  Contributions in Books

            Published

    1. W. Hereman, The Korteweg-de Vries Equation. In: The Princeton Companion to Applied Mathematics, Eds.: N. J. Higham et al, Princeton University Press, Cambridge, MA, Part III.16, p. 150 (2015).
    2. Ü. Göktas and W. Hereman, Symbolic Computation of Conservation Laws, Generalized Symmetries, and Recursion Operators for Nonlinear Differential-Difference Equations. In: Dynamical Systems and Methods, Eds.: A. Luo, J.. Machado, and D. Baleanu, Springer Verlag, New York, Chapter 7, pp. 153-168 (2011).
    3. W. Hereman, P.J. Adams, H.L. Eklund, M.S. Hickman, and B.M. Herbst, Direct Methods and Symbolic Software for Conservation Laws of Nonlinear Equations. In: Advances in Nonlinear Waves and Symbolic Computation, Ed.: Z. Yan, Nova Science Publishers, New York, Chapter 2, pp. 19-79 (2009).
    4. W. Hereman, Shallow Water Waves and Solitary Waves. In: Encyclopedia of Complexity and Systems Science, Ed.: R.A. Meyers, Springer Verlag, Heibelberg, Germany, Entry 480, pp. 8112-8125 (2009). Reprinted in: Mathematics of Complexity and Dynamical Systems -- Selected entries from the Encyclopedia of Complexity and Systems Science, Ed.: R.A. Meyers, Springer Verlag, Heidelberg, Germany, pp. 1520-1532 (2013). Updated version to appear in: Encyclopedia of Complexity and Systems Science - version 2, Ed.: R.A. Meyers, Springer Verlag, Heidelberg, Germany, 2018, online and print editions.
    5. W. Hereman, M. Colagrosso, R. Sayers, A. Ringler, B. Deconinck, M. Nivala, and M.S. Hickman, Continuous and Discrete Homotopy Operators and the Computation of Conservation Laws. In: Differential Equations with Symbolic Computation, Trends in Mathematics, Eds.: D. Wang and Z. Zheng, Birkhäuser Verlag, Basel, Switzerland, Chapter 15, pp. 255-290 (2005).
    6. W. Hereman, Painlevé Theory. In: Computer Algebra Handbook: Foundations, Applications, Systems. Eds.: J. Grabmeier, E. Kaltofen, and V. Weispfenning, Springer Verlag, Berlin, Germany, Ch. 2 (Symbolic Methods for Differential Equations), Section 2.11, Chapter 2, pp. 96-109 (2002).
    7. W. Hereman and Ü. Göktas, Integrability Tests for Nonlinear Evolution Equations, Computer Algebra Systems: A Practical Guide, Chapter 12, Ed.: M. Wester, Wiley and Sons, New York, pp. 211-232 (1999).
    8. W. Hereman, Lie Symmetry Analysis with Symbolic Software. In: Encyclopedia of Mathematics, Supplement Volume I, Ed.: M. Hazewinkel, Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 351-355 (1998).
    9. W. Hereman, Symbolic Software for Lie Symmetry Analysis. In: CRC Handbook of Lie Group Analysis of Differential Equations, Volume 3: New Trends in Theoretical Developments and Computational Methods, Ed.: N.H. Ibragimov, CRC Press, Boca Raton, Florida, Chapter 13, pp. 367-413 (1996).

    4  Featured Book Reviews and Book Reviews

           Published

    1. W. Hereman, Involution: The Formal Theory of Differential Equations and Its Applications in Computer Algebra by Werner Seiler, Springer-Verlag, Heidelberg, 2010, SIAM Review, vol. 53 (3), pp. 589-591 (2011).
    2. W. Hereman, Featured Review: The Mathematica GuideBook for Numerics and the Mathematica GuideBook for Symbolics by Michael Trott, Springer-Verlag, New York, 2006, SIAM Review, vol. 49 (1), pp. 123-129 (2007).
    3. W. Hereman, Featured Review: The Mathematica GuideBook for Programming and the Mathematica GuideBook for Graphics by Michael Trott, Springer-Verlag, New York, 2004, SIAM Review, vol. 47 (4), pp. 801-806 (2006).

    5  In Refereed Journals

            Submitted

    1. F. Verheest and W. A. Hereman, Overtaking interaction of two weakly nonlinear acoustic solitons in plasmas at critical densities (2018).
    2. S. C. Mancas and W. Hereman, Traveling wave solutions to a seventh-order Korteweg-de-Vries equation: I. Sech solutions (2017).
    3. T. Bridgman and W. Hereman, Gauge-equivalent Lax pairs of Boussinesq-type systems of partial difference equations (2017).

           Published

    1. C. P. Olivier, F. Verheest, and W. Hereman, Collision properties of overtaking supersolitons with small amplitudes, Physics of Plasmas, vol. 25(3), art. no. 032309, 6 pages (2018).
    2. F. Verheest, C. P. Olivier, and W. Hereman, Modified Korteweg-de Vries solitons at supercritical densities in two-electron temperature plasmas, Journal of Plasma Physics, vol. 82(2), art. no. 905820208, 13 pages (2016).
    3. T. Bridgman, W. Hereman, G. R. W. Quispel, and P. H. van der Kamp, Symbolic computation of Lax pairs of partial difference equations using consistency around the cube, Foundations of Computational Mathematics, vol. 13 (4), pp. 517-544 (2013).
    4. F. Verheest, M. A. Hellberg, and W. Hereman, Head-on Collisions of Electrostatic Solitons in Multi-Ion Plasmas, Physics of Plasmas, vol. 19 (9), art. no. 092302, 7 pages (2012).
    5. F. Verheest, M. A. Hellberg, and W. Hereman, Head-on Collisions of Electrostatic Solitons in Nonthermal Plasmas, Physical Review E, vol. 86, art. no. 036402, 9 pages (2012).
    6. M. Hickman, W. Hereman, J. Larue, Ü. Göktas, Scaling invariant Lax pairs of nonlinear evolution equations, Applicable Analysis, vol. 91 (2), pp. 381-402 (2012).
    7. D. Poole and W. Hereman, Symbolic computation of conservation laws for nonlinear partial differential equations in multiple space dimensions, Journal of Symbolic Computation, vol. 46 (12), pp. 1355-1377 (2011).
    8. Ü. Göktas and W. Hereman, Symbolic computation of recursion operators for nonlinear differential-difference equations, Mathematical and Computational Applications, vol. 16 (1), pp. 1-12 (2011).
    9. D. Baldwin and W. Hereman, A symbolic algorithm for computing recursion operators of nonlinear partial differential equations, International Journal of Computer Mathematics, vol. 87 (5), pp. 1094-1119 (2010).
    10. W. Hereman, Foreword to the Special Issue on Continuous and Discrete Integrable Systems with Applications, Applicable Analysis, vol. 89 (4), pp. 429-431 (2010).
    11. D. Poole and W. Hereman, The homotopy operator method for symbolic integration by parts and inversion of divergences with applications, Applicable Analysis, vol. 89 (4), pp. 433-455 (2010).
    12. M. Grundland, W. Hereman, and Ï. Yurdusen, Conformally parametrized surfaces associated with CPN sigma models, Journal of Physics A: Mathematical and Theoretical, vol. 41, art. no. 065204, 28 pages (2008).
    13. W. Hereman, B. Deconinck, and L. D. Poole, Continuous and discrete homotopy operators: A theoretical approach made concrete, Mathematics and Computers in Simulation, vol. 74 (4-5), pp. 352-360 (2007).
    14. D. Baldwin and W. Hereman, Symbolic software for the Painlevé test of nonlinear differential ordinary and partial equations, Journal of Nonlinear Mathematical Physics, vol. 13 (1), pp. 90-110 (2006).
    15. W. Hereman, Symbolic computation of conservation laws of nonlinear partial differential equations in multi-dimensions, International Journal of Quantum Chemistry, vol. 106 (1) pp. 278-299 (2006).
    16. D. Baldwin, Ü. Göktas, and W. Hereman, Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations, Computer Physics Communications, vol. 162 (3), pp. 203-217 (2004).
    17. D. Baldwin, Ü. Göktas, W. Hereman, L. Hong, R.S. Martino, and J.C. Miller, Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs, Journal of Symbolic Computation, vol. 37 (6), pp. 669-705 (2004).
    18. M. Hickman and W. Hereman, Computation of densities and fluxes of nonlinear differential-difference equations, Proceedings Royal Society of London A, vol. 459 (2039), pp. 2705-2729 (2003).
    19. J. DeSanto, G. Erdmann, W. Hereman, and M. Misra, Application of wavelet transforms for solving integral equations that arise in rough surface scattering, IEEE Antennas and Propagation Magazine, vol. 43 (6), pp. 55-62 (2001).
    20. J. DeSanto, G. Erdmann, W. Hereman, B. Krause, M. Misra, and E. Swim, Theoretical and computational aspects of scattering from rough surfaces: Two-dimensional transmission surfaces using the spectral-coordinate method, Waves in Random Media, vol. 11 (4), pp. 489-526 (2001).
    21. J. DeSanto, G. Erdmann, W. Hereman, B. Krause, M. Misra, and E. Swim, Theoretical and computational aspects of scattering from rough surfaces: Two-dimensional perfectly reflecting surfaces using the spectral-coordinate method, Waves in Random Media, vol. 11 (4), pp. 455-487 (2001).
    22. J. DeSanto, G. Erdmann, W. Hereman, and M. Misra, Theoretical and computational aspects of scattering from rough surfaces: One-dimensional transmission interface, Waves in Random Media, vol. 11 (4), pp. 425-453 (2001).
    23. F. Verheest, W. Hereman, and W. Malfliet, Comments on "A new mathematical approach for finding the solitary waves in dusty plasma", Physics of Plasmas, vol. 6 (11), pp. 4392-4394 (1999).
    24. Ü. Göktas and W. Hereman, Algorithmic computation of higher-order symmetries for nonlinear evolution and lattice equations, Advances in Computational Mathematics, vol. 11 (1), pp. 55-80 (1999).
    25. L. Monzón, G. Beylkin, and W. Hereman, Compactly supported wavelets based on almost interpolating and nearly linear phase filters (Coiflets), Applied and Computational Harmonic Analysis, vol. 7 (2), pp. 184-210 (1999).
    26. W. Hereman, Ü. Göktas, M. Colagrosso, and A. Miller, Algorithmic integrability tests for nonlinear differential and lattice equations, Computer Physics Communications, vol. 115 (2-3), pp. 428-446 (1998).
    27. Ü. Göktas and W. Hereman, Computation of conservation laws for nonlinear lattices, Physica D, vol. 123 (1-4), pp. 425-436 (1998).
    28. J. DeSanto, G. Erdmann, W. Hereman, and M. Misra, Theoretical and computational aspects of scattering from rough surfaces: One-dimensional perfectly reflecting surfaces, Waves in Random Media, vol. 8 (4), pp. 385-414 (1998).
    29. W. Navidi, W. Murphy, Jr., and W. Hereman, Statistical methods in surveying by trilateration, Computational Statistics and Data Analysis, vol. 27 (2), pp. 209-227 (1998).
    30. Ü. Göktas and W. Hereman, Symbolic computation of conserved densities for systems of nonlinear evolution equations, Journal of Symbolic Computation, vol. 24 (5), pp. 591-621 (1997).
    31. Ü. Göktas, W. Hereman, and G. Erdmann, Computation of conserved densities for systems of nonlinear differential-difference equations, Physics Letters A, vol. 236 (1-2), pp. 30-38 (1997).
    32. W. Hereman, Review of symbolic software for Lie symmetry analysis, Mathematical and Computer Modelling, vol. 25 (8-9), pp. 115-132 (1997).
    33. W. Hereman and A. Nuseir, Symbolic methods to construct exact solutions of nonlinear partial differential equations, Mathematics and Computers in Simulation, vol. 43 (1), pp. 13-27 (1997).
    34. W. Malfliet and W. Hereman, The tanh method: II. Perturbation technique for conservative systems, Physica Scripta, vol. 54 (6), pp. 569-575 (1996).
    35. W. Malfliet and W. Hereman, The tanh method: I. Exact solutions of nonlinear evolution and wave equations, Physica Scripta, vol. 54 (6), pp. 563-568 (1996).
    36. W. Hereman, Computer algebra: lightening the load, Physics World, vol. 9 (3), pp. 47-52, March 1996.
    37. R. Willox, W. Hereman and F. Verheest, Complete integrability of a modified vector derivative nonlinear Schrödinger equation, Physica Scripta, vol. 52, pp. 21-26 (1995).
    38. W. Hereman and W. Zhuang, Symbolic software for soliton theory, Acta Applicandae Mathematicae, vol. 39, pp. 361-378 (1995).
    39. W. Hereman, Visual data analysis: maths made easy, Physics World, vol. 8 (4), pp. 49-53, April 1995.
    40. F. Verheest and W. Hereman, Conservation laws and solitary wave solutions for generalized Schamel equations, Physica Scripta, vol. 50, pp. 611-614 (1994).
    41. W. Hereman, Review of symbolic software for the computation of Lie symmetries of differential equations, Euromath Bulletin, vol. 1 (2), pp. 45-82 (1994).
    42. W. Hereman, W.-H. Steeb, and N. Euler, Comment on: `Towards the conservation laws and Lie symmetries for the Khokhlov-Zabolotskaya equation in three dimensions', Journal of Physics A: Mathematical and General, vol. 25 (8), pp. 2417-2418 (1992).
    43. W.-H. Steeb, N. Euler, and W. Hereman, A note on the Zakharov equation and Lie symmetry vector fields, Nuovo Cimento B (Note Brevi), vol. 107 (10), pp. 1211-1213 (1992).
    44. R.A. Mertens, W. Hereman, and J.-P. Ottoy, Approximate and numerical methods in Acousto-optics : Part 2. Oblique incidence of the light -- Bragg Reflection, Academiae Analecta, vol. 53 (1), pp. 27-59 (1991).
    45. B. Champagne, W. Hereman, and P. Winternitz, The computer calculation of Lie point symmetries of large systems of differential equations, Computer Physics Communications, vol. 66 (2-3), pp. 319-340 (1991).
    46. W. Hereman, Exact solitary wave solutions of coupled nonlinear evolution equations using Macsyma, Computer Physics Communications, vol. 65 (1-3), pp. 143-150 (1991).
    47. W. Hereman and M. Takaoka, Solitary wave solutions of nonlinear evolution and wave equations using a direct method and MACSYMA, Journal of Physics A: Mathematical and General, vol. 23 (21), pp. 4805-4822 (1990).
    48. R.A. Mertens, W. Hereman, and J.-P. Ottoy, The Raman-Nath equations revisited. II. Oblique incidence of the light -- Bragg reflection, Selected Papers on Acousto-optics, Ed.: A. Korpel, SPIE Milestone Series, SPIE Optical Engineering Press, Bellingham, Washington, vol. MS 16, pp. 444-448 (1990).
    49. F. Verheest, W. Hereman, and H. Serras, Possible chaotic pulsations in ZZ Ceti and rapidly oscillating Ap stars due to nonlinear harmonic mode coupling, Monthly Notices of the Royal Astronomical Society, vol. 245, pp. 392-396 (1990).
    50. P.P. Banerjee, F. Daoud and W. Hereman, A straightforward method for finding implicit solitary wave solutions of nonlinear evolution and wave equations, Journal of Physics A: Mathematical and General, vol. 23 (4), pp. 521-536 (1990).
    51. W. Hereman and S. Angenent, The Painlevé test for nonlinear ordinary and partial differential equations, MACSYMA Newsletter, vol. 6 (1), pp. 11-18 (1989).
    52. W. Hereman, P.P. Banerjee, and M. Chatterjee, Derivation and implicit solution of the Harry Dym equation and its connections with the Korteweg-de Vries equation, Journal of Physics A: Mathematical and General, vol. 22 (3), pp. 241-255 (1989).
    53. R.A. Mertens, W. Hereman, and J.-P. Ottoy, Approximate and numerical methods in Acousto-optics: Part 1. Normal incidence of the light, Academiae Analecta, vol. 50 (1), pp. 9-50 (1988).
    54. R. Pieper, A. Korpel, and W. Hereman, Extension of the Acousto-optic Bragg regime through Hamming apodization of the sound field, Journal of the Optical Society of America A: Optics and Image Science, vol. 3 (10), pp. 1608-1619 (1986).
    55. W. Hereman, P.P. Banerjee, A. Korpel, G. Assanto, A. Van Immerzeele, and A. Meerpoel, Exact solitary wave solutions of non-linear evolution and wave equations using a direct algebraic method, Journal of Physics A: Mathematical and General, vol. 19 (5), pp. 607-628 (1986).
    56. W. Hereman, Contribution to the theoretical study of the diffraction of ordinary and laser light by an ultrasonic wave in a liquid, Academiae Analecta, vol. 48 (1), pp. 23-52 (1986).
    57. W. Hereman, A. Korpel, and P.P. Banerjee, A general physical approach to solitary wave construction from linear solutions, Wave Motion, vol. 7 (3), pp. 283-290 (1985).
    58. W. Hereman, R.A. Mertens, F. Verheest, O. Leroy, J.M. Claeys, and E. Blomme, Interaction of light and ultrasound: Acousto-optics, Physicalia Magazine, vol. 6 (4), pp. 213-245 (1984).
    59. R.A. Mertens, W. Hereman. and R. De Spiegeleere, On the exact theory of tops rising by friction, Zeitschrift für Angewandte Mathematik und Mechanik (Journal of Applied Mathematics and Mechanics), vol. 62 (4), pp. T58-T60 (1982).
    60. F. Verheest and W. Hereman, Nonlinear mode decoupling for classes of evolution equations, Journal of Physics A: Mathematical and General, vol. 15 (1), pp. 95-102 (1982).
    61. W. Hereman, F. Verheest, and R.A. Mertens, Acousto-optic diffraction of intense laser light in a liquid, Acustica, vol. 48 (1), pp. 1-9 (1981).
    62. W. Hereman, Diffraction of light by an amplitude-modulated ultrasonic wave at normal and oblique incidence of the light, Simon Stevin, vol. 54 (3-4), pp. 193-211 (1980).
    63. F. Verheest and W. Hereman, Nonresonant mode coupling for classes of Korteweg-de Vries equations, Journal of the Physical Society of Japan, vol. 47 (6), pp. 2007-2012 (1979).
    64. W. Hereman and R.A. Mertens, On the diffraction of light by an amplitude-modulated ultrasonic wave, Wave Motion, vol. 1 (4), pp. 287-298 (1979).

    6  In Refereed Conference Proceedings

    1. Ü. Göktas and W. Hereman, Symbolic computation of conservation laws, generalized symmetries, and recursion operators for nonlinear differential-difference equations, Proceedings of the Third Conference on Nonlinear Science and Complexity (NSC 2010), Ankara, Turkey, July 28-31, 2010, Eds.: D. Baleanu, Z.B. Guvenc, and O. Defterli, Cankaya University Publications, Ankara, Turkey, Symposium 15, Article ID 89, 6 pages.
    2. Ü. Göktas; and W. Hereman, Symbolic computation of recursion operators for nonlinear differential-difference equations, Proceedings of the First International Symposium on Computing in Science and Engineering (ISCSE 2010), Kusadasi, Aydin, Turkey, June 3-5, 2010, Ed.: Ï. Gürler, Gediz University Publications, Izmir, Turkey (2010), pp. 27-33.
    3. J. de la Porte, B.M. Herbst, W. Hereman and S.J. van der Walt, An introduction to diffusion maps, Proceedings of the 19th Symposium of the Pattern Recognition Association of South Africa (PRASA 2008), Cape Town, South Africa, November 26-28, 2008, Ed.: F. Nicolls, University of Cape Town, Cape Town, South Africa (2008), pp. 15-25.
    4. W. Hereman and W. Malfliet, The tanh method: A tool to solve nonlinear partial differential equations with symbolic software, 9th World Multiconference on Systemics, Cybernetics, and Informatics (WMSCI 2005), Eds.: N. Callaos and W. Lesso, Orlando, Florida, July 10-13, 2005, vol. 3, pp. 165-168.
    5. W. Hereman, J.A. Sanders, J. Sayers, and J.P. Wang, Symbolic computation of polynomial conserved densities, generalized symmetries, and recursion operators for nonlinear differential-difference equations, Group Theory and Numerical Analysis, CRM Proceedings and Lecture Series 39, Eds.: P. Winternitz, D. Gomez-Ullate, A. Iserles, D. Levi, P.J. Olver, R. Quispel, and P. Tempesta, American Mathematical Society, Providence, Rhode Island (2005), pp. 133-148.
    6. D. Baldwin, W. Hereman, and J. Sayers, Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs, Group Theory and Numerical Analysis, CRM Proceedings and Lecture Series 39, Eds.: P. Winternitz, D. Gomez-Ullate, A. Iserles, D. Levi, P.J. Olver, R. Quispel, and P. Tempesta, American Mathematical Society, Providence, Rhode Island (2005), pp. 17-32.
    7. M. Hickman and W. Hereman, Computation of densities and fluxes of nonlinear differential-difference equations, Proceedings Sixth Asian Symposium on Computer Mathematics, Beijing China, April 17-19, 2003, Eds. Z. Li and W. Sit, World Scientific Publishing, Singapore (2003), pp. 163-173.
    8. Ü. Göktas and W. Hereman, Invariants and symmetries for partial differential equations and lattices, Proceedings Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation, Ed.: J.A. DeSanto, Colorado School of Mines, Golden, Colorado, June 1-5, 1998, SIAM, Philadelphia (1998), pp. 403-407.
    9. W. Hereman and W. Zhuang, Symbolic software for soliton theory, Proceedings of Conference KdV '95, April 1995, Amsterdam, The Netherlands, Eds.: M. Hazewinkel, H.W. Capel, and E.M. de Jager, Kluwer Academic Publishers, Dordrecht, The Netherlands (1995), pp. 361-378.
    10. W. Hereman, L. Marchildon, and M. Grundland, Lie point symmetries of classical field theories, Proceedings of the XIX International Colloquium, Salamanca, Spain, June 29-July 4, 1992, Anales de Física. Monografías, Group Theoretical Methods in Physics, vol. 1, Eds.: M.A. del Olmo, M. Santander, and J. Mateos Guilarte, Real Sociedad Española de Física, Madrid, Spain (1993), pp. 402-405.
    11. W. Hereman, SYMMGRP.MAX and other symbolic programs for Lie symmetry analysis of partial differential equations, Exploiting Symmetry in Applied and Numerical Analysis, Lectures in Applied Mathematics 29, Proceedings of the AMS-SIAM Summer Seminar, Fort Collins, July 26-August 1, 1992, Eds.: E. Allgower, K. Georg, and R. Miranda, American Mathematical Society, Providence, Rhode Island (1993), pp. 241-257.
    12. W. Hereman and W. Zhuang, Symbolic computation of solitons with Macsyma, Computational and Applied Mathematics II: Differential Equations. Eds.: W.F. Ames and P.J. van der Houwen, North Holland, Amsterdam The Netherlands (1992), pp. 287-296.
    13. F. Verheest and W. Hereman, Chaotic pulsations in variable stars with harmonic mode coupling, Research Reports in Physics, Nonlinear Dynamics, Proceedings of the Conference on Aspects of Nonlinear Dynamics: Solitons and Chaos, Free University of Brussels, Brussels, Belgium, December 6-8, 1990, Eds.: I. Antoniou and F.J. Lambert, Springer Verlag, Berlin Germany (1991), pp. 166-170.
    14. R.A. Mertens, W. Hereman, and J.-P. Ottoy, The N-th order approximation method in acousto-optics and the condition for 'pure' Bragg reflection, Proceedings of the Symposium on Physical Acoustics: Fundamental and Applications, University of Leuven at Kortrijk, Kortrijk, Belgium, June 19-22, 1990, Eds.: O. Leroy and M.A. Breazeale, Plenum Press, New York (1991), pp. 505-509.
    15. W. Hereman and W. Zhuang, A MACSYMA program for the Hirota method, Proceedings of the 13th IMACS World Congress on Computation and Applied Mathematics, Dublin, July 22-26, 1991, Eds.: R. Vichnevetsky and J.J.H. Miller, Criterion Press, Dublin Ireland (1991), vol. 2, pp. 842-843. Also available: W. Hereman and W. Zhuang, Symbolic computation of solitons via Hirota's bilinear method, Technical Report, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado (1994), 33 pages.
    16. W. Hereman, Application of a Macsyma program for the Painlevé test to the Fitzhugh-Nagumo equation, Partially Integrable Evolution Equations in Physics, Proceedings of the Summer School for Theoretical Physics, Les Houches, France, March 21-28, 1989, Eds.: R. Conte and N. Boccara, Kluwer Academic Publishers, Dordrecht, The Netherlands (1990), Contributed Papers, pp. 585-586.
    17. W. Hereman and E. Van den Bulck, MACSYMA program for the Painlevé test of nonlinear ordinary and partial differential equations, Proceedings of the Workshop on Finite Dimensional Integrable Nonlinear Dynamical Systems, Eds.: P.G.L. Leach and W.-H. Steeb, Johannesburg, South Africa, January 11-15, 1988. World Scientific, Singapore (1988), pp. 117-129.
    18. A. Defebvre, R.A. Mertens, J.-P. Ottoy and W. Hereman, Experimental testing of truncated Raman-Nath system solutions, Proceedings Ultrasonics International '87, London, United Kingdom, July 6-9, 1987, Butterworth-Heinemann, Oxford, United Kingdom (1987), pp. 78-83.
    19. R.A. Mertens, W. Hereman, and J.-P. Ottoy, The Raman-Nath equations revisited. II. Oblique incidence of the light - Bragg reflection, Proceedings Ultrasonics International '87, London, United Kingdom, July 6-9, 1987, Butterworth-Heinemann, Oxford, United Kingdom (1987), pp. 84-89.
    20. R.A. Mertens, J.-P. Ottoy, and W. Hereman, Numerical integration of the truncated Raman-Nath system, Congress Proceedings of the 12th International Congress on Acoustics, Toronto, Canada, July 24-31, 1986, vol. 2, p. G7-1.
    21. R.A. Mertens, W. Hereman and J.-P. Ottoy, The Raman-Nath equations revisited, Proceedings Ultrasonics International '85, London, United Kingdom, July 2-5, 1985, Butterworths, Guildford, United Kingdom (1985), pp. 422-428.
    22. R.A. Mertens and W. Hereman, On the diffraction of light by adjacent parallel ultrasonic waves. A general theory, Proceedings Ultrasonics International '83, Halifax, Canada, July 12-14, 1983, Butterworths, Guildford, United Kingdom (1983) pp. 282-288.
    23. W. Hereman, Acousto-optic diffraction of intense laser light in an isotropic medium (including third harmonic generation), Proceedings of the Second Spring School on Acousto-optics and Applications, Gdansk, Poland, May 24-29, 1983, pp. 206-223.
    24. R.A. Mertens and W. Hereman, Diffraction of light by ultrasonic waves in the case of oblique incidence of the light. General theory and approximations, Proceedings of the Second Spring School on Acousto-optics and Applications, Gdansk, Poland, May 24-29, 1983, pp. 9-31.
    25. W. Hereman and R.A. Mertens, On the diffraction of light by ultrasonic waves in the Bragg case, Revue d'Acoustique, 11th International Congress on Acoustics, Paris, France, July 19-27, 1983, vol. 2, pp. 287-290.
    26. W. Hereman, F. Verheest and R.A. Mertens, On the Acousto-optics of an intense laser beam in a liquid, Proceedings Ultrasonics International '81, Brighton, United Kingdom, June 30-July 2, 1981, Butterworths, Guildford, United Kingdom (1981) pp. 104-109.
    27. R.A. Mertens, W. Hereman, and F. Verheest, Some recent developments in the theory of diffraction of light by ultrasonic waves, Proceedings of the First Spring School on Acousto-optics and Applications, Gdansk, Poland, May 26-30, 1980, pp. 33-51.
    28. F. Verheest and W. Hereman, Limitations of the description of nonlinear plasma phenomena through wave-wave interaction, Proceedings International Conference on Plasma Physics, Nagoya, Japan, April 7-11, 1980, l0P-II-01, vol. 1, p. 386.
    29. R.A. Mertens and W. Hereman, Über die Raman-Nathsche Theorie der Beugung des Lichtes an Ultraschallwellen, Fortschritte der Akustik DAGA '80, München, Germany, March 10-13, 1980, VDE-Verlag, Berlin, Germany (1980), pp. 563-566.

    7  In Unrefereed Conference Proceedings

    1. W. Hereman and A. Nuseir, Symbolic methods to find exact solutions of nonlinear PDEs, Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, Atlanta, Georgia, July 11-15, 1994, Ed.: W.F. Ames, IMACS, New Brunswick (1994), vol. 1, pp. 222-225.
    2. W. Hereman, Symbolic software for the study of nonlinear partial differential equations , Advances in Computer Methods for Partial Differential Equations VII, Proceedings of the 7th IMACS International Conference on Computer Methods for Partial Differential Equations, Rutgers University, New Brunswick, New Jersey, June 22-24, 1992, Eds.: R. Vichnevetsky, D. Knight, and G. Richter, IMACS, New Brunswick, New Jersey (1993), pp. 326-332.
    3. W. Hereman, Solitary wave solutions of coupled nonlinear evolution equations using Macsyma, Proceedings of IMACS 1st International Conference on Computational Physics, Eds.: K. Gustafson and W. Wyss, University of Colorado, Boulder, Colorado, June 11-15, 1990, pp. 150-153.
    4. R.A. Mertens, W. Hereman, F. Verheest, and J.-P. Ottoy, Theoretical acousto-optics: exact, approximate and numerical methods, "Book of Abstracts", Proceedings of Workshop V on (nonlinear) stability, University of Antwerp, Antwerp, Belgium, September 11-23, 1990, Ed.: D.K. Callebaut, UIA Press, Antwerp, Belgium (1990), pp. 45-50.
    5. W. Hereman, The construction of implicit and explicit solitary wave solutions of nonlinear partial differential equations, Proceedings of the Conference on Applied Mathematics in Honor of Professor A.A. Ashour, 3-6 January, 1987, Cairo, Egypt (1988), pp. 291-312.
    6. W. Hereman, P.P. Banerjee, and D. Faker, The construction of solitary wave solutions of the Korteweg-de Vries equation via Painlevé analysis, Proceedings of Workshop WASDA III: Wave and Soliton Days Antwerp, University of Antwerp, June 2-3, 1988, Eds.: D.K. Callebaut and W. Malfliet, UIA Press, Antwerp, Belgium (1988), vol. II, pp. 166-191.
    7. P.P. Banerjee, W. Choe, G. Cao, and W. Hereman, Stationary eigenmodes and their stability during wave propagation in a medium with quadratic and cubic nonlinearities without dispersion, Proceedings of Workshop WASDA III: Wave and Soliton Days Antwerp, Antwerp, Belgium, June 2-3, 1988, Eds.: D.K. Callebaut and W. Malfliet, UIA Press, Antwerp, Belgium (1988), vol. II, pp. 143-165.
    8. F. Verheest and W. Hereman, Wave decoupling for the Sharma-Tasso-Olver and higher-order Korteweg-de Vries equations, Proceedings of Workshop II on (nonlinear) Stability in Magneto-hydro-dynamics, University of Antwerp, Antwerp, Belgium, September 1-30, 1980, Ed.: D.K. Callebaut, UIA Press, Antwerp, Belgium (1980), pp. 125-137.

    8  Technical Reports

    1. J. DeSanto, G. Erdmann, W. Hereman, B. Krause, M. Misra, and E. Swim, Theoretical and computational aspects of scattering from rough surfaces: Two-dimensional surfaces, Technical Report # 4 MURI Project, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado (1980), 183 pages.
    2. J. DeSanto, G. Erdmann, W. Hereman, and M. Misra, Theoretical and computational aspects of scattering from rough surfaces: One-dimensional transmission interface, Technical Report # 3 MURI Project, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado (2000), 121 pages.
    3. J. DeSanto, G. Erdmann, W. Hereman, and M. Misra, Theoretical and computational aspects of scattering from rough surfaces: One-dimensional perfectly reflecting surfaces, Technical Report MCS-97-09 MURI Project, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado (1997), 62 pages.
    4. J. Boleng, C. Craig, J. DeSanto, G. Erdmann, W. Hereman, M. Khebchareon, M. Misra, and A. Sinex, Computational modeling of rough surface scattering, Technical Report MCS-96-09 MURI Project, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado (1996), 40 pages.
    5. W. Murphy and W. Hereman, Determination of a position in three dimensions using trilateration and approximate distances, Technical Report MCS-95-07, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado (1995), 19 pages.
    6. W. Hereman and W. Murphy, Manual for Trilateration Program: Determination of a position in three dimensions using trilateration and approximate distances, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado (1991), 22 pages.
    7. W. Hereman and W. Zhuang, Symbolic computation of solitons via Hirota's bilinear method, Technical Report, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado (1994), 33 pages.
    8. W. Hereman, Y. Nagel and J. Strikwerda, Macsyma at CMS version 309.3: An introduction to symbolic mathematical computation, CMS Technical Summary Report # 88-3, Department of Mathematics & Center for the Mathematical Sciences, The University of Wisconsin, Madison, Wisconsin (1987), 21 pages.

    9  Theses

    1. W. Hereman, Theoretische Aspecten van Akoesto-Optische Diffractie (Theoretical Aspects of Acousto-optical Diffraction), Ph.D. Dissertation, University of Ghent, Ghent, Belgium, June 1982, 247 pages, 5 figures, in Dutch.
    2. W. Hereman, Asymtotische Storingsmethodes in de Studie van Niet-lineaire Resonanties (The Krylov-Bugoliubov-Mitropolski Method and the Two-Timescales Averaging Method for the Study of Nonlinear Dynamical Resonances), Master of Science Thesis, University of Ghent, Ghent, Belgium (1976), 215 pages, in Dutch.

    10  Research Monographs

    1. W. Hereman, Theoretische Aspecten van Akoesto-Optische Diffractie (Theoretical Aspects of Acousto-optical Diffraction), Research Monograph, prepared for the Royal Academy of Sciences, Literature and Fine Arts of Belgium; University of Ghent, Ghent, Belgium (1985), 260 pages, 5 figures, in Dutch.
    2. W. Hereman, Een Bijdrage tot de Theoretische Studie van de Diffractie van Gewoon en Laserlicht door een Ultrageluidsgolf in een Vloeistof, Thesis written for a Contest of the Royal Academy of Sciences, Literature and Fine Arts of Belgium; University of Ghent, Ghent, Belgium (1984), 143 pages, in Dutch.

    11  Ph.D. Dissertations and Masters Theses of Hereman's Students

    1. T.J. Bridgman, Symbolic Computation of Lax Pairs of Nonlinear Partial Difference Equations , Ph.D. Thesis, Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, Colorado, August 2018 (defended: April 2018).
    2. J. Rezac, Computation of Scaling Invariant Lax Pairs with Applications to Conservation Laws , Masters Thesis, Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, Colorado, May 2012 (defended: March 2012).
    3. J. Larue, Symbolic Verification of Operator and Matrix Lax Pairs for Some Completely Integrable Nonlinear Partial Differential Equations , Masters Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, June 2011 (defended: March 2011).
    4. L.D. Poole, Symbolic Computation of Conservation Laws of Nonlinear Partial Differential Equations using Homotopy Operators , Ph.D. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, December 2009 (defended: April 2009).
    5. P. Adams, Symbolic Computation of Conserved Densities and Fluxes for Nonlinear Systems of Partial Differential Equations with Transcendental Nonlinearities , M.S. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, May 2003.
    6. D. Baldwin, Symbolic Algorithms and Software for the Painlevé Test and Recursion Operators for Nonlinear Partial Differential Equations , M.S. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, May 2004.
    7. H. Eklund Symbolic Computation of Conserved Densities and Fluxes for Nonlinear Systems of Differential-difference Equations , M.S. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, May 2003.
    8. Ü. Göktas, Algorithmic Computation of Symmetries, Invariants and Recursion Operators for Systems of Nonlinear Evolution and Differential-difference Equations , Ph.D. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, May 1998.
    9. Ü. Göktas, Symbolic Computation of Conserved Densities for Systems of Evolution Equations , M.S. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, May 1996.
    10. W. Murphy, Determination of a Position Using Approximate Distances and Trilateration , M.S. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, May 1992.
    11. A. Nuseir, Symbolic Computation of Exact Solutions of Nonlinear Partial Differential Equations using Direct Methods , Ph.D. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, May 1995.
    12. W. Zhuang, Symbolic Computation of Exact Solutions of Nonlinear Evolution and Waves Equations , M.S. Thesis, Department of Mathematical and Computer Sciences, Colorado School of Mines, Golden, Colorado, December 1991.

    This material is based upon work supported by the National Science Foundation (NSF) under Grants Nos. CCF-0830783, CCR-9300978, CCR-9625421, CCR-9901929, DMS-9732069, DMS-9912293, and CCF-0830783; and by the Air Force Office of Scientific Research under Grant F49620-96-1-0039. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of NSF or AFOSR.
    Willy Hereman

    Last updated: Sunday, June 10, 2018, at 1:30pm