"/*********************************************************/"
"/*    WELCOME TO THE MATHEMATICA PROGRAM HIROTA.M        */"
"/*            BY WILLY HEREMAN AND WUNING ZHUANG         */"
"/*              FOR THE CALCULATION OF SOLITONS          */"
"/*           OF THE ""Parameter"" 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 "
kpar*Derivative[0, 0, 0, 1][f][x, y, z, t]^2 - 
   kpar*f[x, y, z, t]*Derivative[0, 0, 0, 2][f][x, y, z, t] - 
   3*Derivative[1, 0, 0, 1][f][x, y, z, t]*
    Derivative[2, 0, 0, 0][f][x, y, z, t] + 
   3*Derivative[1, 0, 0, 0][f][x, y, z, t]*
    Derivative[2, 0, 0, 1][f][x, y, z, t] + 
   Derivative[0, 0, 0, 1][f][x, y, z, t]*
    Derivative[3, 0, 0, 0][f][x, y, z, t] + 
   10*Derivative[3, 0, 0, 0][f][x, y, z, t]^2 - 
   f[x, y, z, t]*Derivative[3, 0, 0, 1][f][x, y, z, t] - 
   15*Derivative[2, 0, 0, 0][f][x, y, z, t]*
    Derivative[4, 0, 0, 0][f][x, y, z, t] + 
   6*Derivative[1, 0, 0, 0][f][x, y, z, t]*
    Derivative[5, 0, 0, 0][f][x, y, z, t] - 
   f[x, y, z, t]*Derivative[6, 0, 0, 0][f][x, y, z, t]" = 0"
"For this equation the polynomial P(K,-OMEGA,L)= "
  K^6 - K^3*OMEGA + kpar*OMEGA^2
"The equation has at least a one- and two-soliton solution."
"For the ""Parameter"" equation, "
"there are "2" different dispersion relations;"
"the first one is: "-(Sqrt[-K[i]^6 + K[0]^3*M[0]]/Sqrt[kpar])
"we use the dispersion relation: "
" OMEGA[I] = "(K[I]^3 - Sqrt[K[I]^6 - 4*kpar*K[I]^6])/(2*kpar)
"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"] = "6
"for this test K["2"] = "8
"for this test K["3"] = "14
"The equation did not pass the random number test(s) for "
"the existence of a "3" soliton solution."
"The condition "(-69318195335474537771827200*(1 + 5*kpar)*
     (-1 + Sqrt[1 - 4*kpar] + 2*kpar + 2*kpar^2))/kpar^3" = 0 must be \
satisfied."
"Starting the construction of the two-soliton solution."
"The coefficient a[I,J] is calculated via the polynomial form."
"The polynomial is P[K,-OMEGA,L] = "K^6 - K^3*OMEGA + kpar*OMEGA^2
"The coefficient a[I,J] = "(-3*K[I]^5*K[J] + 12*kpar*K[I]^5*K[J] + 
     3*K[I]^2*Sqrt[K[I]^6 - 4*kpar*K[I]^6]*K[J] + 3*K[I]^4*K[J]^2 - 
     30*kpar*K[I]^4*K[J]^2 - 3*K[I]*Sqrt[K[I]^6 - 4*kpar*K[I]^6]*K[J]^2 - 
     K[I]^3*K[J]^3 + 40*kpar*K[I]^3*K[J]^3 + 3*K[I]^2*K[J]^4 - 
     30*kpar*K[I]^2*K[J]^4 - 3*K[I]*K[J]^5 + 12*kpar*K[I]*K[J]^5 + 
     Sqrt[K[I]^6 - 4*kpar*K[I]^6]*Sqrt[K[J]^6 - 4*kpar*K[J]^6] - 
     3*K[I]^2*K[J]*Sqrt[K[J]^6 - 4*kpar*K[J]^6] + 
     3*K[I]*K[J]^2*Sqrt[K[J]^6 - 4*kpar*K[J]^6])/
   (-3*K[I]^5*K[J] + 12*kpar*K[I]^5*K[J] + 
     3*K[I]^2*Sqrt[K[I]^6 - 4*kpar*K[I]^6]*K[J] - 3*K[I]^4*K[J]^2 + 
     30*kpar*K[I]^4*K[J]^2 + 3*K[I]*Sqrt[K[I]^6 - 4*kpar*K[I]^6]*K[J]^2 - 
     K[I]^3*K[J]^3 + 40*kpar*K[I]^3*K[J]^3 - 3*K[I]^2*K[J]^4 + 
     30*kpar*K[I]^2*K[J]^4 - 3*K[I]*K[J]^5 + 12*kpar*K[I]*K[J]^5 + 
     Sqrt[K[I]^6 - 4*kpar*K[I]^6]*Sqrt[K[J]^6 - 4*kpar*K[J]^6] + 
     3*K[I]^2*K[J]*Sqrt[K[J]^6 - 4*kpar*K[J]^6] + 
     3*K[I]*K[J]^2*Sqrt[K[J]^6 - 4*kpar*K[J]^6])
"The function f = "1 + E^THETA[1] + E^THETA[2] + 
   E^(THETA[1] + THETA[2])*a[1, 2]
"At the end of the computations the form of the function f"
"and the coefficient a[1,2] 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."