Time= 30 msecs

(D2)              CSM$USERS:[WHEREMAN.HIROTA]H_ITOB4.OUT;1

(C3) batchload("hir_sing.max")$

Batching the file hir_sing.max
Batchload done.

Time= 4250 msecs

(C4) n:3$

Time= 0 msecs

(C5) B(f,g):= Dxt[1,1](f,g) + Dxt[2,2](f,g)$

Time= 0 msecs

(C6) name:Ito_b4$

Time= 0 msecs

(C7) hirota(b,name,n,3,1,true,true)$

/*********************************************************/

/*    WELCOME TO THE MACSYMA PROGRAM HIR_SING.MAX       */

/*            BY WILLY HEREMAN AND WUNING ZHUANG         */

/*              FOR THE CALCULATION OF SOLITONS          */

/*             OF THE  ITO_B4  EQUATION                 */

/*              WITH HIROTA'S METHOD                     */

/*     Version 1.0, released on May 29, 1995             */

/*********************************************************/

The equation in f corresponding to the given bilinear operator is 


 2   2        3                      4             3           2           2
d F d F      d F   dF   dF dF       d F       dF  d F         d F  2      d F
--- --- - 2 ------ -- - -- -- + F ------- - 2 -- ------ + 2 (-----)  + F ----- 
  2   2       2    dX   dT dX       2   2     dT      2      dT dX       dT dX
dT  dX      dT  dX                dT  dX         dT dX

                                                                             = 0


                                                   2      2
For this equation the polynomial P(K,-OMEGA,L) =  K  OMEGA  - K OMEGA

The equation has at least a one- and two-soliton solution.

For the  ITO_B4  equation, 

there are  2  different dispersion relations.

          1
[OMEGA  = --, OMEGA  = 0]
      I   K        I
           I

We use the dispersion relation 

             1
 OMEGA[I] =  --
             K
              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   =  4
 1

K   =  21
 2

K   =  19
 3

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.

                                    2      2
The polynomial is P(K,-OMEGA,L) =  K  OMEGA  - K OMEGA

                                     2   2            2
                            (K  - K )  (K  - K  K  + K )
                              J    I     J    I  J    I
The coefficient a[i,j] =  - ----------------------------
                                     2   2            2
                            (K  + K )  (K  + K  K  + K )
                              J    I     J    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= 14370 msecs

(C8) kill(all)$

Time= 30 msecs

(C1) closefile();