(D21) CSM$USERS:[WHEREMAN.PROGRAMS.NPAINLEVE.SINGLE]P_BURG.OUT;1 (C22) batch("np_exec.max"); (C23) /* ************************************************************************* */ /* Batch file NP_EXEC.MAX */ /* ************************************************************************* */ exec_painleve (eq, alpha, do_resonances, max_resonance, do_simplification)$ You are using the simplification suggested by KRUSKAL You selected G(T,X,...) = X - H(T,...) ---------------------------------------------------------------- PAINLEVE ANALYSIS OF EQUATION, - A F + F F + F = 0 X X X T ---------------------------------------------------------------- ALPHA SUBSTITUTE U G FOR f IN ORIGINAL EQUATION. 0 MINIMUM POWERS OF g ARE [2 ALPHA - 1, ALPHA - 2] 2 ALPHA - 1 2 * COEFFICIENT OF G IS U ALPHA 0 NOTE : THIS TERM VANISHES FOR ALPHA = 0 , VERIFY IF ALPHA = 0 LEADS TO DOMINANT BEHAVIOR, IF IT DOES THEN RUN THE PROGRAM AGAIN WITH THIS USER SUPPLIED VALUE OF ALPHA. HENCE, PUT BETA = 0 . ALPHA - 2 * COEFFICIENT OF G IS - U A (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 ( 2 ALPHA - 1 ) AND ( ALPHA - 2 ) OF g, WITH alpha = - 1 , POWER OF g is - 3 ----> SOLVE FOR U 0 1 TERM - U (2 A + U ) -- IS DOMINANT 0 0 3 G IN EQUATION. ---------------------------------------------------------------- 1 ) WITH U = - 2 A ----> FIND RESONANCES 0 ALPHA R + ALPHA SUBSTITUTE U G + U G FOR f IN EQUATION 0 R R - 3 TERM ( - A (R - 2) (R + 1) ) U G IS DOMINANT R IN EQUATION. THE ONLY NON-NEGATIVE INTEGRAL ROOT IS [R = 2] WITH MAXIMUM RESONANCE = 2 ----> CHECK RESONANCES. 2 ==== \ K - 1 SUBSTITUTE POWER SERIES > G U FOR f IN EQUATION. / K ==== K = 0 WITH U = - 2 A 0 1 * COEFFICIENT OF -- IS - 2 A (H - U ) 2 T 1 G U = H 1 T 1 * COEFFICIENT OF - IS 0 G U IS ARBITRARY ! 2 COMPATIBILITY CONDITION IS SATISFIED ! ---------------------------------------------------------------- (C24) 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 <= [2] 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() > ---------------------------------------------------------------- (C25) /* ************************** END of NP_EXEC.MAX ************************** */ (D25) DONE (C26) closefile();