"/*********************************************************/"
"/*    WELCOME TO THE MATHEMATICA PROGRAM HIROTA.M        */"
"/*            BY WILLY HEREMAN AND WUNING ZHUANG         */"
"/*              FOR THE CALCULATION OF SOLITONS          */"
"/*           OF THE ""Ito-b6"" 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[0, 1, 0, 0][f][x, y, z, t]^2 - 
   f[x, y, z, t]*Derivative[0, 2, 0, 0][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] - 
   f[x, y, z, t]*Derivative[3, 0, 0, 1][f][x, y, z, t]" = 0"
"For this equation the polynomial P(K,-OMEGA,L)= "L^2 - K^3*OMEGA + OMEGA^2
"The equation has at least a one- and two-soliton solution."
"For the ""Ito-b6"" equation, "
"we use the dispersion relation: "
" OMEGA[I] = "(K[I]^3 - Sqrt[K[I]^6 - 4*L[I]^2])/2
"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"] = "11
"for this test K["2"] = "17
"for this test K["3"] = "15
"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"] = "17
"The equation did not pass the random number test(s) for "
"the existence of a "3" soliton solution."
"The condition "(211770408960*(724825354023715646284102610035629840377291469\
8079314476260834806490 + 16340278391279231149326177969864526048288601891942\
752968917959434*Sqrt[196765] + 
       2147739665147855761193387802638133025983185117881331402176262410*
        Sqrt[11389469] + 14753312004055446010532060164928950036199826367406\
16445606823829*Sqrt[24137245] + 
       16629745634682916305221401736832093238948907316295601413482900*
        Sqrt[189974600497] + 4841809664312671473689638407381519214193803805\
852614860295938*Sqrt[2241048867785] + 
       437157353940672686718872042208863068544735567024262512640548*
        Sqrt[274910403672905] + 
       4927582088934391057090041734171810858573110898443538080125*
        Sqrt[2163709823147966093]))/
   ((1331 + 3*Sqrt[196765])^6*(3375 + Sqrt[11389469])^6*
     (4913 + Sqrt[24137245])^6)" = 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] = "L^2 - K^3*OMEGA + OMEGA^2
"The coefficient a[I,J] = "(-3*K[I]^5*K[J] + 3*K[I]^4*K[J]^2 - 
     K[I]^3*K[J]^3 + 3*K[I]^2*K[J]^4 - 3*K[I]*K[J]^5 + 
     3*K[I]^2*K[J]*Sqrt[K[I]^6 - 4*L[I]^2] - 
     3*K[I]*K[J]^2*Sqrt[K[I]^6 - 4*L[I]^2] + 4*L[I]*L[J] - 
     3*K[I]^2*K[J]*Sqrt[K[J]^6 - 4*L[J]^2] + 
     3*K[I]*K[J]^2*Sqrt[K[J]^6 - 4*L[J]^2] + 
     Sqrt[K[I]^6 - 4*L[I]^2]*Sqrt[K[J]^6 - 4*L[J]^2])/
   (-3*K[I]^5*K[J] - 3*K[I]^4*K[J]^2 - K[I]^3*K[J]^3 - 3*K[I]^2*K[J]^4 - 
     3*K[I]*K[J]^5 + 3*K[I]^2*K[J]*Sqrt[K[I]^6 - 4*L[I]^2] + 
     3*K[I]*K[J]^2*Sqrt[K[I]^6 - 4*L[I]^2] + 4*L[I]*L[J] + 
     3*K[I]^2*K[J]*Sqrt[K[J]^6 - 4*L[J]^2] + 
     3*K[I]*K[J]^2*Sqrt[K[J]^6 - 4*L[J]^2] + 
     Sqrt[K[I]^6 - 4*L[I]^2]*Sqrt[K[J]^6 - 4*L[J]^2])
"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."