/* Edited output file, some comments taken out */

(C18) N:3$

(C19) B1(F,G):=DXT[0,1](F,G)+DX[3](F,G)$

(C20) B2(F,G):=DX[2](F,G)$

(C21) NAME:MKDV$

(C22) HIROTA(B1,B2,NAME,N,TRUE,TRUE,TRUE)$

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

/*      WELCOME TO THE MACSYMA PROGRAM HIROTA_SYSTEM     */

/*       WRITTEN BY WILLY HEREMAN AND WUNING ZHUANG      */

/*        FOR THE CALCULATION OF SOLITON SOLUTIONS       */

/*          OF THE  MKDV  EQUATION          */

/*              WITH HIROTA'S METHOD                     */

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

/*                Copyright 1995                         */

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

There is at least a one or two soliton solutions!

In the expansions THETA = K X - OMEGA T + CONSTANT.

For the  MKDV  equation, the dispersion relation is 

           3
  OMEGA = K

Starting the test for the existence of a three soliton solution!

There also exists a three soliton solution!

Starting the test for the existence of a four soliton solution

There also exists a four soliton solution!

Starting the construction of the three soliton solution!

The coefficient A      is calculated via the polynomial form.
                 I, J

                        2
The polynomial is P2 = K

                                   2
                          (K  - K )
                            J    I
The coefficient A      =  ----------
                 I, J              2
                          (K  + K )
                            J    I

The coefficient  B         is calculated via the polynomial form.
                  1, 2, 3

                                      2          2          2
                             (K2 - K1)  (K3 - K1)  (K3 - K2)
The coefficient  B        =  --------------------------------
                  1, 2, 3             2          2          2
                             (K2 + K1)  (K3 + K1)  (K3 + K2)

                                 THETA  + THETA  + THETA
                                      3        2        1
The function f = - %I B        %E
                       1, 2, 3

           THETA  + THETA            THETA  + THETA         THETA
                3        2                3        1             3
 - A     %E                - A     %E                + %I %E
    2, 3                      1, 3

           THETA  + THETA         THETA         THETA
                2        1             2             1
 - A     %E                + %I %E       + %I %E       + 1
    1, 2

                               THETA  + THETA  + THETA
                                    3        2        1
The function g = %I B        %E
                     1, 2, 3

           THETA  + THETA            THETA  + THETA         THETA
                3        2                3        1             3
 - A     %E                - A     %E                - %I %E
    2, 3                      1, 3

           THETA  + THETA         THETA         THETA
                2        1             2             1
 - A     %E                - %I %E       - %I %E       + 1
    1, 2

Starting the verification of the coefficients

The coefficient AA      is calculated via the bilinear operator.
                  I, J

                                    2
                           (K  - K )
                             J    I
The coefficient AA      =  ----------
                  I, J              2
                           (K  + K )
                             J    I

The coefficients A      and AA      are the same!
                  I, J        I, J

The coefficient BB         is calculated via the bilinear operator.
                  1, 2, 3

                                       2          2          2
                              (K  - K )  (K  - K )  (K  - K )
                                2    1     3    1     3    2
The coefficient BB         =  --------------------------------
                  1, 2, 3              2          2          2
                              (K  + K )  (K  + K )  (K  + K )
                                2    1     3    1     3    2

The coefficients  B        and  BB        are the same!
                   1, 2, 3        1, 2, 3

Time= 277300 msecs

(C23) A[1,2]:FACTOR(A[1,2]);

                                            2
                                   (K2 - K1)
(D23)                              ----------
                                            2
                                   (K2 + K1)
(C24) B[1,2,3]:FACTOR(B[1,2,3]);

                                 2          2          2
                        (K2 - K1)  (K3 - K1)  (K3 - K2)
(D24)                   --------------------------------
                                 2          2          2
                        (K2 + K1)  (K3 + K1)  (K3 + K2)
(C25) F;

                      THETA  + THETA  + THETA            THETA  + THETA
                           3        2        1                3        2
(D25) - %I B        %E                         - A     %E
            1, 2, 3                               2, 3

           THETA  + THETA         THETA            THETA  + THETA         THETA
                3        1             3                2        1             2
 - A     %E                + %I %E       - A     %E                + %I %E
    1, 3                                    1, 2

        THETA
             1
 + %I %E       + 1

(C26) G;

                    THETA  + THETA  + THETA            THETA  + THETA
                         3        2        1                3        2
(D26) %I B        %E                         - A     %E
          1, 2, 3                               2, 3

           THETA  + THETA         THETA            THETA  + THETA         THETA
                3        1             3                2        1             2
 - A     %E                - %I %E       - A     %E                - %I %E
    1, 3                                    1, 2

        THETA
             1
 - %I %E       + 1

(C27) CLOSEFILE();