Time= 50 msecs (D2) CSM$USERS:[WHEREMAN.HIROTA]H_BOUS.OUT;1 (C3) batchload("hir_sing.max")$ Batching the file hir_sing.max Batchload done. Time= 4670 msecs (C4) n:3$ Time= 0 msecs (C5) B(f,g):= Dxt[0,2](f,g) - Dx[2](f,g) - Dx[4](f,g)$ Time= 0 msecs (C6) name:Boussinesq$ Time= 0 msecs (C7) hirota(b,name,n,1,1,true,false)$ /*********************************************************/ /* WELCOME TO THE MACSYMA PROGRAM HIR_SING.MAX */ /* BY WILLY HEREMAN AND WUNING ZHUANG */ /* FOR THE CALCULATION OF SOLITONS */ /* OF THE BOUSSINESQ 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 4 3 2 2 2 d F dF d F d F 2 d F dF 2 d F dF 2 F --- - 4 -- --- + 3 (---) + F --- - (--) - F --- + (--) = 0 4 dX 3 2 2 dX 2 dT dX dX dX dX dT 2 4 2 For this equation the polynomial P(K,-OMEGA,L) = OMEGA - K - K The equation has at least a one- and two-soliton solution. For the BOUSSINESQ equation, there are 2 different dispersion relations. 2 2 [OMEGA = - K SQRT(K + 1), OMEGA = K SQRT(K + 1)] I I I I I I We use the dispersion relation 2 OMEGA[I] = - K SQRT(K + 1) I I 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): K = 17 1 K = 11 2 K = 13 3 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): K = 11 1 K = 4 2 K = 8 3 K = 22 4 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. 2 4 2 The polynomial is P(K,-OMEGA,L) = OMEGA - K - K 2 2 2 2 SQRT(K + 1) SQRT(K + 1) - 2 K + 3 K K - 2 K - 1 I J J I J I The coefficient a[i,j] = ----------------------------------------------------- 2 2 2 2 SQRT(K + 1) SQRT(K + 1) - 2 K - 3 K K - 2 K - 1 I J J I J I The coefficient b[1,2,3] is calculated via the polynomial form. 2 2 2 2 The coefficient b[1,2,3] = (SQRT(K + 1) SQRT(K + 1) - 2 K + 3 K K - 2 K 1 2 2 1 2 1 2 2 2 2 - 1) (SQRT(K + 1) SQRT(K + 1) - 2 K + 3 K K - 2 K - 1) 1 3 3 1 3 1 2 2 2 2 (SQRT(K + 1) SQRT(K + 1) - 2 K + 3 K K - 2 K - 1) 2 3 3 2 3 2 2 2 2 2 /((SQRT(K + 1) SQRT(K + 1) - 2 K - 3 K K - 2 K - 1) 1 2 2 1 2 1 2 2 2 2 (SQRT(K + 1) SQRT(K + 1) - 2 K - 3 K K - 2 K - 1) 1 3 3 1 3 1 2 2 2 2 (SQRT(K + 1) SQRT(K + 1) - 2 K - 3 K K - 2 K - 1)) 2 3 3 2 3 2 THETA + THETA + THETA THETA + THETA 3 2 1 3 2 The function f = B %E + A %E 1, 2, 3 2, 3 THETA + THETA THETA THETA + THETA THETA 3 1 3 2 1 2 + A %E + %E + A %E + %E 1, 3 1, 2 THETA 1 + %E + 1 At the end of the computations the form of the function f and the coefficients a[i,j] and b[1,2,3] are available. The explicit factored form of a[1,2] and b[1,2,3] can be obtained by entering factor(a[1,2]); and factor(b[1,2,3]); The explicit forms of theta[i] and omega[i] are also available. The form of f can be obtained by typing f; . The explicit form of f can be obtained by typing expression(f); . Time= 55000 msecs (C8) kill(all)$ Time= 30 msecs (C1) closefile();