"/*********************************************************/"
"/*    WELCOME TO THE MATHEMATICA PROGRAM HIROTA.M        */"
"/*            BY WILLY HEREMAN AND WUNING ZHUANG         */"
"/*              FOR THE CALCULATION OF SOLITONS          */"
"/*           OF THE ""KdV"" 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]*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 - K*OMEGA
"The equation has at least a one- and two-soliton solution."
"For the ""KdV"" equation, "
"we use the dispersion relation: "
" OMEGA[I] = "K[I]^3
"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"] = "7
"for this test K["2"] = "2
"for this test K["3"] = "13
"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 "
4" soliton solution."
"Wavenumbers K[I] selected for the random number test(s): "
"for this test K["1"] = "17
"for this test K["2"] = "6
"for this test K["3"] = "20
"for this test K["4"] = "10
"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 - K*OMEGA
"The coefficient a[I,J] = "(K[I] - K[J])^2/(K[I] + K[J])^2
"The coefficient b[1,2,3] is calculated via the polynomial form."
"The coefficient b[1,2,3] = "((K[1] - K[2])^2*(K[1] - K[3])^2*
     (K[2] - K[3])^2)/((K[1] + K[2])^2*(K[1] + K[3])^2*(K[2] + 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."
"This is U[X,T] "2*(-((E^(-T + X) + (5*E^((-125*T)/64 + (5*X)/4))/4 + 
           (3*E^((-27*T)/8 + (3*X)/2))/2 + E^((-189*T)/64 + (9*X)/4)/36 + 
           E^((-35*T)/8 + (5*X)/2)/10 + E^((-341*T)/64 + (11*X)/4)/44 + 
           E^((-405*T)/64 + (15*X)/4)/65340)^2/
        (1 + E^(-T + X) + E^((-125*T)/64 + (5*X)/4) + 
           E^((-27*T)/8 + (3*X)/2) + E^((-189*T)/64 + (9*X)/4)/81 + 
           E^((-35*T)/8 + (5*X)/2)/25 + E^((-341*T)/64 + (11*X)/4)/121 + 
           E^((-405*T)/64 + (15*X)/4)/245025)^2) + 
     (E^(-T + X) + (25*E^((-125*T)/64 + (5*X)/4))/16 + 
        (9*E^((-27*T)/8 + (3*X)/2))/4 + E^((-189*T)/64 + (9*X)/4)/16 + 
        E^((-35*T)/8 + (5*X)/2)/4 + E^((-341*T)/64 + (11*X)/4)/16 + 
        E^((-405*T)/64 + (15*X)/4)/17424)/
      (1 + E^(-T + X) + E^((-125*T)/64 + (5*X)/4) + E^((-27*T)/8 + (3*X)/2) + 
        E^((-189*T)/64 + (9*X)/4)/81 + E^((-35*T)/8 + (5*X)/2)/25 + 
        E^((-341*T)/64 + (11*X)/4)/121 + E^((-405*T)/64 + (15*X)/4)/245025))