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

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

(C5) /* The NLS equation : */
 
/* number of independent variables: */

p : 2 $

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

q : 2 $

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

m : 2 $

(C8) parameters:[]$

(C9) sublisteqs:[all]$

(C10) info_given:false$

(C11) subst_deriv_of_vi:true$

(C12) highest_derivatives:all$

(C13) warnings:true$

(C14) e1 : u[1,[0,1]]+(u[1]^2+u[2]^2)*u[2]+u[2,[2,0]];

                                       2    2
(D14)                U          + U  (U  + U ) + U
                      2, [2, 0]    2   2    1     1, [0, 1]


(C15) e2 : u[2,[0,1]]-(u[1]^2+u[2]^2)*u[1]-u[1,[2,0]];

                                       2    2
(D15)                U          - U  (U  + U ) - U
                      2, [0, 1]    1   2    1     1, [2, 0]


(C16) v1 : u[1,[0,1]];

(D16)                              U
                                    1, [0, 1]

(C17) v2 : u[2,[0,1]];

(D17)                              U
                                    2, [0, 1]

(C19) 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                      */

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

You are using the 2 equations of the system.

*** Number of determining equations before simplifications: 46 . ***

*** Number of determining equations after simplifications: 20 . ***

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

(C20) printeqn(lode)$

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

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

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

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

              d
Equation 5 : --- (ETA ) = 0
             dU      1
               1

              2
             d
Equation 6 : --- (PHI ) = 0
               2     1
             dU
               2

              2
             d
Equation 7 : --- (PHI ) = 0
               2     2
             dU
               1

              2
             d
Equation 8 : --- (PHI ) = 0
               2     2
             dU
               2

                2
               d
Equation 9 : ------- (PHI ) = 0
             dU  dU      1
               1   2

                 2
                d
Equation 10 : ------- (PHI ) = 0
              dU  dU      2
                1   2

               2
              d
Equation 11 : --- (PHI ) = 0
                2     1
              dU
                1

Equation 12 :

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

Equation 13 :

 d            d
--- (PHI ) + --- (PHI ) = 0
dU      2    dU      1
  1            2

Equation 14 :

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

Equation 15 :

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

Equation 16 :

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

Equation 17 :

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

Equation 18 :

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

Equation 19 :

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

       2   d             3   d             3   d             2      d
 + U  U  (--- (PHI )) + U  (--- (PHI )) - U  (--- (PHI )) - U  U  (--- (PHI ))
    1  2  dU      1      1  dU      1      2  dU      1      1  2  dU      1
            2                 2                 1                    1

           2                   2
 + 3 PHI  U  + 2 PHI  U  U  + U  PHI  = 0
        2  2        1  1  2    1    2

Equation 20 :

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

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

         2                          2
 - PHI  U  - 2 U  PHI  U  - 3 PHI  U  = 0
      1  2      1    2  2        1  1


(C21) /* save("lodenls.lsp",lode)$ */

closefile();