"/*********************************************************/"
"/*    WELCOME TO THE MATHEMATICA PROGRAM HIROTA.M        */"
"/*            BY WILLY HEREMAN AND WUNING ZHUANG         */"
"/*              FOR THE CALCULATION OF SOLITONS          */"
"/*           OF THE ""Kadomtsev-Petviashvili"" 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 "
3*Derivative[0, 1, 0, 0][f][x, y, z, t]^2 - 
   3*f[x, y, z, t]*Derivative[0, 2, 0, 0][f][x, y, z, t] + 
   Derivative[0, 0, 0, 1][f][x, y, z, t]*
    Derivative[1, 0, 0, 0][f][x, y, z, t] - 
   f[x, y, z, t]*Derivative[1, 0, 0, 1][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^4 + 3*L^2 - K*OMEGA
"The equation has at least a one- and two-soliton solution."
"For the ""Kadomtsev-Petviashvili"" equation, "
"we use the dispersion relation: "
" OMEGA[I] = "(K[I]^4 + 3*L[I]^2)/K[I]
"In the Expansion of f we use THETA = K X - OMEGA T + L Y + 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"] = "18
"for this test K["2"] = "11
"for this test K["3"] = "14
"Wavenumbers L[I] selected for the random number test(s): "
"for this test L["1"] = "13
"for this test L["2"] = "18
"for this test L["3"] = "7
"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"] = "3
"for this test K["2"] = "9
"for this test K["3"] = "17
"Wavenumbers L[I] selected for the random number test(s): "
"for this test L["1"] = "19
"for this test L["2"] = "16
"for this test L["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"] = "7
"for this test K["2"] = "4
"for this test K["3"] = "17
"for this test K["4"] = "2
"Wavenumbers L[I] selected for the random number test(s): "
"for this test L["1"] = "17
"for this test L["2"] = "3
"for this test L["3"] = "7
"for this test L["4"] = "20
"The equation passed the random number test(s) for the existence"
"of a "4" 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"] = "15
"for this test K["2"] = "19
"for this test K["3"] = "2
"for this test K["4"] = "7
"Wavenumbers L[I] selected for the random number test(s): "
"for this test L["1"] = "13
"for this test L["2"] = "9
"for this test L["3"] = "4
"for this test L["4"] = "18
"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^4 + 3*L^2 - K*OMEGA
"The coefficient a[I,J] = "((K[I]^2*K[J] - K[I]*K[J]^2 + K[J]*L[I] - 
       K[I]*L[J])*(K[I]^2*K[J] - K[I]*K[J]^2 - K[J]*L[I] + K[I]*L[J]))/
   ((K[I]^2*K[J] + K[I]*K[J]^2 + K[J]*L[I] - K[I]*L[J])*
     (K[I]^2*K[J] + K[I]*K[J]^2 - K[J]*L[I] + K[I]*L[J]))
"The coefficient b[1,2,3] is calculated via the polynomial form."
"The coefficient b[1,2,3] = "((K[1]^2*K[2] - K[1]*K[2]^2 + K[2]*L[1] - 
       K[1]*L[2])*(K[1]^2*K[2] - K[1]*K[2]^2 - K[2]*L[1] + K[1]*L[2])*
     (K[1]^2*K[3] - K[1]*K[3]^2 + K[3]*L[1] - K[1]*L[3])*
     (K[1]^2*K[3] - K[1]*K[3]^2 - K[3]*L[1] + K[1]*L[3])*
     (K[2]^2*K[3] - K[2]*K[3]^2 + K[3]*L[2] - K[2]*L[3])*
     (K[2]^2*K[3] - K[2]*K[3]^2 - K[3]*L[2] + K[2]*L[3]))/
   ((K[1]^2*K[2] + K[1]*K[2]^2 + K[2]*L[1] - K[1]*L[2])*
     (K[1]^2*K[2] + K[1]*K[2]^2 - K[2]*L[1] + K[1]*L[2])*
     (K[1]^2*K[3] + K[1]*K[3]^2 + K[3]*L[1] - K[1]*L[3])*
     (K[1]^2*K[3] + K[1]*K[3]^2 - K[3]*L[1] + K[1]*L[3])*
     (K[2]^2*K[3] + K[2]*K[3]^2 + K[3]*L[2] - K[2]*L[3])*
     (K[2]^2*K[3] + K[2]*K[3]^2 - K[3]*L[2] + K[2]*L[3]))
"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."