(D3)              CSM$USERS:[WHEREMAN.NSFSYMMETRY]S_KDV.OUT;1

(C4) batch("s_kdv.dat")$

(C5) /* Data file for the Korteweg-de Vries equation */
/* For use with SYMMGRP.MAX */

/* number of independent variables: */

p : 2$

(C6) /* number of dependent variables: */

q : 1$

(C7) /* number of equations in the system: */

m : 1$

(C8) warnings:false$

(C9) parameters : [b] $

(C10) sublisteqs :[all]$

(C11) subst_deriv_of_vi:true$

(C12) highest_derivatives : all$

(C13) info_given : false$

(C14) e1 : u[1,[0,1]]+bb*u[1]*u[1,[1,0]]+u[1,[3,0]];

(D14)              U  U          BB + U          + U
                    1  1, [1, 0]       1, [3, 0]    1, [0, 1]

(C15) /* bb is just a constant parameter */

v1 : u[1,[0,1]];

(D15)                              U
                                    1, [0, 1]

(C17) symmetry(1,0,0)$

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

/*      WELCOME TO THE MACSYMA PROGRAM FOR THE           */

/*         CALCULATION OF THE SYMMETRY GROUP             */

/*                 IN BATCH MODE                         */

/*       WRITTEN BY B. CHAMPAGNE AND W. HEREMAN          */

/*         Project Supervision: P. WINTERNITZ            */

/*        Version 2.0 released on May 29, 1995           */

/*                   Copyright 1991                      */

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

*** Number of determining equations before simplifications: 21 . ***

*** Number of determining equations after simplifications: 8 . ***

*** These determining equations are stored in LODE. ***


(C18) printeqn(lode)$

              d
Equation 1 : --- (ETA ) = 0
             dU      2
               1

              d
Equation 2 : --- (ETA ) = 0
             dX      2
               1

              d
Equation 3 : --- (ETA ) = 0
             dU      1
               1

              2
             d
Equation 4 : --- (PHI ) = 0
               2     1
             dU
               1

Equation 5 :

 d               d
--- (ETA ) - 3 (--- (ETA )) = 0
dX      2       dX      1
  2               1

Equation 6 :

   2              2
  d              d
------- (PHI ) - --- (ETA ) = 0
dU  dX      1      2     1
  1   1          dX
                   1

Equation 7 :

                                   3
     d                d           d
U  (--- (PHI )) BB + --- (PHI ) + --- (PHI ) = 0
 1  dX      1        dX      1      3     1
      1                2          dX
                                    1

Equation 8 :

                                                          3
     d                    d                              d
U  (--- (ETA )) BB - U  (--- (ETA )) BB + PHI  BB + 3 (------- (PHI ))
 1  dX      2         1  dX      1           1               2     1
      2                    1                           dU  dX
                                                         1   1

                                                                3
                                                   d           d
                                                - --- (ETA ) - --- (ETA ) = 0
                                                  dX      1      3     1
                                                    2          dX
                                                                 1

(C19) save("lodekdv.lsp",lode)$

(C20) closefile();