(D15) CSM$USERS:[WHEREMAN.PROGRAMS.NPAINLEVE.SINGLE]P_SASHA.OUT;2 (C16) batch("np_exec.max")$ (C17) /* ************************************************************************* */ /* Batch file NP_EXEC.MAX */ /* ************************************************************************* */ exec_painleve (eq, alpha, do_resonances, max_resonance, do_simplification)$ You are using the simplification suggested by KRUSKAL You selected G(T,X,...) = X - H(T,...) ---------------------------------------------------------------- PAINLEVE ANALYSIS OF EQUATION, F + 2 F F + F + 4 F F Y Y Y X X X Y X X X X Y X X X Y + 6 F F - 2 F = 0 X Y X X T X X ---------------------------------------------------------------- ALPHA SUBSTITUTE U G FOR f IN ORIGINAL EQUATION. 0 MINIMUM POWERS OF g ARE [2 ALPHA - 4, ALPHA - 5] 2 ALPHA - 4 * COEFFICIENT OF G IS 2 2 - 6 U (ALPHA - 1) ALPHA (2 ALPHA - 3) H 0 Y 3 NOTE : THIS TERM VANISHES FOR [ALPHA = -, ALPHA = 0, ALPHA = 1] , 2 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. ALPHA - 5 * COEFFICIENT OF G IS - U (ALPHA - 4) (ALPHA - 3) (ALPHA - 2) 0 (ALPHA - 1) ALPHA H Y NOTE : THIS TERM VANISHES FOR [ALPHA = 0, ALPHA = 1, ALPHA = 2, ALPHA = 3, ALPHA = 4] , 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 ( 2 ALPHA - 4 ) AND ( ALPHA - 5 ) OF g, WITH alpha = - 1 , POWER OF g is - 6 ----> SOLVE FOR U 0 1 TERM - 60 (U - 2) U H -- IS DOMINANT 0 0 Y 6 G IN EQUATION. ---------------------------------------------------------------- 1 ) WITH U = 2 ----> FIND RESONANCES 0 ALPHA R + ALPHA SUBSTITUTE U G + U G FOR f IN EQUATION 0 R R - 6 TERM ( - H (R - 6) (R - 5) (R - 4) (R - 1) (R + 1) ) U G Y R IS DOMINANT IN EQUATION. THE 4 NON-NEGATIVE INTEGRAL ROOTS ARE [R = 1, R = 4, R = 5, R = 6] WITH MAXIMUM RESONANCE = 6 ----> CHECK RESONANCES. 6 ==== \ K - 1 SUBSTITUTE POWER SERIES > G U FOR f IN EQUATION. / K ==== K = 0 WITH U = 2 0 1 * COEFFICIENT OF -- IS 0 5 G U IS ARBITRARY ! 1 COMPATIBILITY CONDITION IS SATISFIED ! 1 3 * COEFFICIENT OF -- IS 12 ((H ) + 6 U H - 2 H - 2 U ) 4 Y 2 Y T 1 G Y 3 (H ) - 2 H - 2 U Y T 1 Y U = - -------------------- 2 6 H Y 1 * COEFFICIENT OF -- IS 12 H (H + 4 U ) 3 Y Y Y 3 G H Y Y U = - ---- 3 4 1 * COEFFICIENT OF -- IS 0 2 G U IS ARBITRARY ! 4 COMPATIBILITY CONDITION IS SATISFIED ! 1 * COEFFICIENT OF - IS 0 G U IS ARBITRARY ! 5 COMPATIBILITY CONDITION IS SATISFIED ! * COEFFICIENT OF 1 IS 0 U IS ARBITRARY ! 6 COMPATIBILITY CONDITION IS SATISFIED ! ---------------------------------------------------------------- (C18) 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 <= [6] and 1 <= l <= [1] ) 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 <= [1] ) 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 <= [1] ) j stands for j_th alpha,k stands for k_th solution set for u[0] ---------------------------------------------------------------- TO SEE THIS MENU AGAIN JUST TYPE < output() > ---------------------------------------------------------------- (C19) /* ************************** END of NP_EXEC.MAX ************************** */ (C20) closefile();