(D13)     CSM$USERS:[WHEREMAN.PROGRAMS.NPAINLEVE.SINGLE]P_SIMODE.OUT;1


(C14) batch("np_exec.max")$


(C15) /* ************************************************************************* */
/*                           Batch file NP_EXEC.MAX                          */
/* ************************************************************************* */

exec_painleve (eq, alpha, do_resonances, max_resonance, do_simplification)$

  SUBSTITUTE  X ----> G + X0

----------------------------------------------------------------

                                        3
PAINLEVE ANALYSIS OF EQUATION,  F    - F   = 0
                                 G G

----------------------------------------------------------------

                  ALPHA
  SUBSTITUTE  U  G       FOR f IN ORIGINAL EQUATION.
               0

  MINIMUM POWERS OF g ARE  [3 ALPHA, ALPHA - 2]

                       3 ALPHA         3
    * COEFFICIENT OF  G         IS  - U
                                       0

                       ALPHA - 2
    * COEFFICIENT OF  G           IS  U  (ALPHA - 1) ALPHA
                                       0

    NOTE : THIS TERM VANISHES FOR   [ALPHA = 0, ALPHA = 1] ,

    VERIFY IF ANY OF THESE VALUES FOR ALPHA LEADS TO DOMINANT

    BEHAVIOR,

    IF IT DOES THEN RUN THE PROGRAM AGAIN WITH THIS VALUE

    AS USER SUPPLIED ALPHA, CALLED BETA.

----------------------------------------------------------------

  FOR EXPONENTS ( 3 ALPHA ) AND ( ALPHA - 2 ) OF g,

    WITH alpha =  - 1 , POWER OF g is  - 3  ----> SOLVE FOR  U
                                                              0

                    2      1
       TERM  - U  (U  - 2) --  IS DOMINANT
                0   0       3
                           G

       IN EQUATION.

----------------------------------------------------------------

1 )  WITH  U  = - SQRT(2)  ----> FIND RESONANCES
            0

                    ALPHA         R + ALPHA
    SUBSTITUTE  U  G       +  U  G           FOR f IN EQUATION
                 0             R

                                    R - 3
       TERM ( (R - 4) (R + 1) ) U  G       IS DOMINANT
                                 R

       IN EQUATION.

       THE ONLY NON-NEGATIVE INTEGRAL ROOT IS  [R = 4]

 

    WITH MAXIMUM RESONANCE =  4  ----> CHECK RESONANCES.

                              4
                             ====
                             \         K - 1
    SUBSTITUTE POWER SERIES   >    U  G       FOR f IN EQUATION.
                             /      K
                             ====
                             K = 0

    WITH U  = - SQRT(2)
          0

                         1
        * COEFFICIENT OF -- IS  - 6 U
                          2          1
                         G

        U  = 0
         1

                         1
        * COEFFICIENT OF - IS  - 6 U
                         G          2

        U  = 0
         2

        * COEFFICIENT OF 1 IS  - 4 U
                                    3

        U  = 0
         3

        * COEFFICIENT OF G IS  0

        U  IS ARBITRARY !
         4

       COMPATIBILITY CONDITION IS SATISFIED !

----------------------------------------------------------------

2 )  WITH  U  = SQRT(2)  ----> FIND RESONANCES
            0

                    ALPHA         R + ALPHA
    SUBSTITUTE  U  G       +  U  G           FOR f IN EQUATION
                 0             R

                                    R - 3
       TERM ( (R - 4) (R + 1) ) U  G       IS DOMINANT
                                 R

       IN EQUATION.

       THE ONLY NON-NEGATIVE INTEGRAL ROOT IS  [R = 4]

 

    WITH MAXIMUM RESONANCE =  4  ----> CHECK RESONANCES.

                              4
                             ====
                             \         K - 1
    SUBSTITUTE POWER SERIES   >    U  G       FOR f IN EQUATION.
                             /      K
                             ====
                             K = 0

    WITH U  = SQRT(2)
          0

                         1
        * COEFFICIENT OF -- IS  - 6 U
                          2          1
                         G

        U  = 0
         1

                         1
        * COEFFICIENT OF - IS  - 6 U
                         G          2

        U  = 0
         2

        * COEFFICIENT OF 1 IS  - 4 U
                                    3

        U  = 0
         3

        * COEFFICIENT OF G IS  0

        U  IS ARBITRARY !
         4

       COMPATIBILITY CONDITION IS SATISFIED !

----------------------------------------------------------------


(C16) output()$

----------------------------------------------------------------

AT THE END OF THE COMPUTATIONS THE FOLLOWING ARE AVAILABLE:

* U VALUE(S)

  (type uval[j,k,l] where 1 <= j <=  1 and 0 <= k <=  [4]

  and 1 <= l <=  [2] )

  j stands for j_th alpha,k stands for u[k],l stands for

  l_th solution set for u[0] 

* ALPHA VALUE(S)

  (type alpha[j] where 1 <= j <=  1 )

  j stands for j_th alpha

* COMPATIBILITY CONDITION(S)

  (type compcond[j,k] where 1 <= j <=  1 and 1 <= k <=  [2] )

  j stands for j_th alpha,k stands for k_th solution set for u[0]

* RESONANCE(S)

  (type res[j,k] where 1 <= j <=  1 and 1 <= k <=  [2] )

  j stands for j_th alpha,k stands for k_th solution set for u[0]

----------------------------------------------------------------

TO SEE THIS MENU AGAIN JUST TYPE < output() >

----------------------------------------------------------------



(C17) /* ************************** END of NP_EXEC.MAX ************************** */



(C18) closefile();