"/*********************************************************/"
"/*    WELCOME TO THE MATHEMATICA PROGRAM HIROTA.M        */"
"/*            BY WILLY HEREMAN AND WUNING ZHUANG         */"
"/*              FOR THE CALCULATION OF SOLITONS          */"
"/*           OF THE ""Boussinesq"" EQUATION                   */"
"/*              WITH HIROTA'S METHOD                     */"
"/*     Version 1.0 firts released on May 29, 1995        */"
"/*      Last updated on January 25, 2007                 */"
"/*               Copyright 1995-2007                     */"
"/*********************************************************/"
"The equation in f corresponding to the given bilinear operator is "
Derivative[0, 0, 0, 1][f][x, y, z, t]^2 - 
   f[x, y, z, t]*Derivative[0, 0, 0, 2][f][x, y, z, t] - 
   Derivative[1, 0, 0, 0][f][x, y, z, t]^2 + 
   f[x, y, z, t]*Derivative[2, 0, 0, 0][f][x, y, z, t] + 
   3*Derivative[2, 0, 0, 0][f][x, y, z, t]^2 - 
   4*Derivative[1, 0, 0, 0][f][x, y, z, t]*
    Derivative[3, 0, 0, 0][f][x, y, z, t] + 
   f[x, y, z, t]*Derivative[4, 0, 0, 0][f][x, y, z, t]" = 0"
"For this equation the polynomial P(K,-OMEGA,L)= "-K^2 - K^4 + OMEGA^2
"The equation has at least a one- and two-soliton solution."
"For the ""Boussinesq"" equation, "
"we use the dispersion relation: "
" OMEGA[I] = "-(K[I]*Sqrt[1 + K[I]^2])
"In the Expansion of f we use THETA = K X - OMEGA T + CST."
"Starting the random test(s) for the existence of a "
3" soliton solution."
"Wavenumbers K[I] selected for the random number test(s): "
"for this test K["1"] = "4
"for this test K["2"] = "17
"for this test K["3"] = "14
"The equation passed the random number test(s) for the existence"
"of a "3" soliton solution."
"Starting the random test(s) for the existence of a "
3" soliton solution."
"Wavenumbers K[I] selected for the random number test(s): "
"for this test K["1"] = "6
"for this test K["2"] = "3
"for this test K["3"] = "10
"The equation passed the random number test(s) for the existence"
"of a "3" soliton solution."
"Starting the symbolic test for the existence of a "
3" soliton solution."
"The equation passed the symbolic test for the existence"
"of a "3" soliton solution."
"Starting the random test(s) for the existence of a "
4" soliton solution."
"Wavenumbers K[I] selected for the random number test(s): "
"for this test K["1"] = "10
"for this test K["2"] = "6
"for this test K["3"] = "4
"for this test K["4"] = "8
"The equation passed the random number test(s) for the existence"
"of a "4" soliton solution."
"Starting the construction of the three-soliton solution."
"The coefficient a[I,J] is calculated via the polynomial form."
"The polynomial is P[K,-OMEGA,L] = "-K^2 - K^4 + OMEGA^2
"The coefficient a[I,J] = "(-1 - 2*K[I]^2 + 3*K[I]*K[J] - 2*K[J]^2 + 
     Sqrt[1 + K[I]^2]*Sqrt[1 + K[J]^2])/
   (-1 - 2*K[I]^2 - 3*K[I]*K[J] - 2*K[J]^2 + 
     Sqrt[1 + K[I]^2]*Sqrt[1 + K[J]^2])
"The coefficient b[1,2,3] is calculated via the polynomial form."
"The coefficient b[1,2,3] = "((-1 - 2*K[1]^2 + 3*K[1]*K[2] - 2*K[2]^2 + 
       Sqrt[1 + K[1]^2]*Sqrt[1 + K[2]^2])*
     (-1 - 2*K[1]^2 + 3*K[1]*K[3] - 2*K[3]^2 + 
       Sqrt[1 + K[1]^2]*Sqrt[1 + K[3]^2])*
     (-1 - 2*K[2]^2 + 3*K[2]*K[3] - 2*K[3]^2 + 
       Sqrt[1 + K[2]^2]*Sqrt[1 + K[3]^2]))/
   ((-1 - 2*K[1]^2 - 3*K[1]*K[2] - 2*K[2]^2 + 
       Sqrt[1 + K[1]^2]*Sqrt[1 + K[2]^2])*
     (-1 - 2*K[1]^2 - 3*K[1]*K[3] - 2*K[3]^2 + 
       Sqrt[1 + K[1]^2]*Sqrt[1 + K[3]^2])*
     (-1 - 2*K[2]^2 - 3*K[2]*K[3] - 2*K[3]^2 + 
       Sqrt[1 + K[2]^2]*Sqrt[1 + K[3]^2]))
"The function f = "1 + E^THETA[1] + E^THETA[2] + E^THETA[3] + 
   E^(THETA[1] + THETA[2])*a[1, 2] + E^(THETA[1] + THETA[3])*a[1, 3] + 
   E^(THETA[2] + THETA[3])*a[2, 3] + 
   E^(THETA[1] + THETA[2] + THETA[3])*b[1, 2, 3]
"At the end of the computations the form of the function f"
"and the coefficients a[i,j] and b[1,2,3] are explicitly available."
"The explicit forms of OMEGA[i] and THETA[i] are also available."
"The Explicit form of f can be obtained by typing EXPRF."