Time= 40 msecs (C3) batchload("hir_sing.max")$ Batching the file hir_sing.max Batchload done. Time= 4270 msecs (C4) N:3$ Time= 0 msecs (C5) /* kpar:-1/5; */ B(f,g):=kpar*Dt[2](f,g)+Dxt[3,1](f,g)+Dx[6](f,g)$ Time= 0 msecs (C6) name:Parameter_Dependent$ Time= 0 msecs (C7) hirota(B,name,N,2,2,true,true)$ /*********************************************************/ /* WELCOME TO THE MACSYMA PROGRAM HIR_SING.MAX */ /* BY WILLY HEREMAN AND WUNING ZHUANG */ /* FOR THE CALCULATION OF SOLITONS */ /* OF THE PARAMETER_DEPENDENT 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 2 6 5 2 4 3 3 d F dF 2 d F dF d F d F d F d F 2 dF d F F --- KPAR - (--) KPAR + F --- - 6 -- --- + 15 --- --- - 10 (---) - -- --- 2 dT 6 dX 5 2 4 3 dT 3 dT dX dX dX dX dX dX 2 2 3 4 d F d F d F dF d F + 3 ----- --- - 3 ------ -- + F ------ = 0 dT dX 2 2 dX 3 dX dT dX dT dX 2 3 6 For this equation the polynomial P(K,-OMEGA,L) = KPAR OMEGA - K OMEGA + K The equation has at least a one- and two-soliton solution. For the PARAMETER_DEPENDENT equation, there are 2 different dispersion relations. 3 3 3 3 K SQRT(1 - 4 KPAR) - K K SQRT(1 - 4 KPAR) + K I I I I [OMEGA = - ------------------------, OMEGA = ------------------------] I 2 KPAR I 2 KPAR We use the dispersion relation 3 3 K SQRT(1 - 4 KPAR) - K I I OMEGA[I] = - ------------------------ 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): K = 7 1 K = 10 2 K = 17 3 The equation did not pass the random number test(s) for the existence of a 3 soliton solution. The condition - 10431350890154887133952000000 (5 KPAR + 1) 2 3 (2 KPAR + 2 KPAR + SQRT(1 - 4 KPAR) - 1)/KPAR = 0 must be satisfied. Starting the construction of the two-soliton solution. The coefficient a[i,j] is calculated via the polynomial form. 2 3 6 The polynomial is P(K,-OMEGA,L) = KPAR OMEGA - K OMEGA + K 2 2 2 The coefficient a[i,j] = (K - K ) (4 K KPAR - 2 K K KPAR + 4 K KPAR J I J I J I 2 2 2 + K SQRT(1 - 4 KPAR) + K K SQRT(1 - 4 KPAR) + K SQRT(1 - 4 KPAR) - K J I J I J 2 2 2 2 - K K - K )/((K + K ) (4 K KPAR + 2 K K KPAR + 4 K KPAR I J I J I J I J I 2 2 2 + K SQRT(1 - 4 KPAR) - K K SQRT(1 - 4 KPAR) + K SQRT(1 - 4 KPAR) - K J I J I J 2 + K K - K )) I J I THETA + THETA THETA THETA 2 1 2 1 The function f = A %E + %E + %E + 1 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 factored form of a[1,2] can be obtained by typing factor(a[1,2]); 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= 35720 msecs (C8) kill(all)$ Time= 40 msecs (C1) closefile();