"/*********************************************************/"
"/*    WELCOME TO THE MACSYMA PROGRAM HIROTA_SINGLE.MAX   */"
"/*            BY WILLY HEREMAN AND WUNING ZHUANG         */"
"/*              FOR THE CALCULATION OF SOLITONS          */"
"/*           OF THE ""7th_order_KdV"" EQUATION                   */"
"/*              WITH HIROTA'S METHOD                     */"
"/*     Version 1.0 released on May 29, 1995              */"
"/*                   Copyright 1995                      */"
"/*********************************************************/"
"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] + 
   35*Derivative[4, 0, 0, 0][f][x, y, z, t]^2 - 
   56*Derivative[3, 0, 0, 0][f][x, y, z, t]*
    Derivative[5, 0, 0, 0][f][x, y, z, t] + 
   28*Derivative[2, 0, 0, 0][f][x, y, z, t]*
    Derivative[6, 0, 0, 0][f][x, y, z, t] - 
   8*Derivative[1, 0, 0, 0][f][x, y, z, t]*
    Derivative[7, 0, 0, 0][f][x, y, z, t] + 
   f[x, y, z, t]*Derivative[8, 0, 0, 0][f][x, y, z, t]" = 0"
"For this equation the polynomial P(K,-OMEGA,L)= "K^8 - K*OMEGA
"The equation has at least a one- and two-soliton solution."
"For the ""7th_order_KdV"" equation, "
"we use the dispersion relation: "
" OMEGA[I] = "K[I]^7
"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"] = "19
"for this test K["2"] = "5
"for this test K["3"] = "9
"The equation did not pass the random number test(s) for "
"the existence of a "3" soliton solution."
"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^8 - K*OMEGA
"The coefficient a[I,J] = "((-K[I] + K[J])^2*(K[I]^2 - K[I]*K[J] + K[J]^2)^2)/
   ((K[I] + K[J])^2*(K[I]^2 + K[I]*K[J] + K[J]^2)^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."