(D13) CSM$USERS:[WHEREMAN.PROGRAMS.NPAINLEVE.SINGLE]P_RAM3.OUT;1 (C14) batch("np_exec.max"); (C15) /* ************************************************************************* */ /* Batch file NP_EXEC.MAX */ /* ************************************************************************* */ exec_painleve (eq, alpha, do_resonances, max_resonance, do_simplification)$ SUBSTITUTE X ----> G + X0 ---------------------------------------------------------------- 2 PAINLEVE ANALYSIS OF EQUATION, F + F = 0 G ---------------------------------------------------------------- ALPHA SUBSTITUTE U G FOR f IN ORIGINAL EQUATION. 0 MINIMUM POWERS OF g ARE [2 ALPHA, ALPHA - 1] 2 ALPHA 2 * COEFFICIENT OF G IS U 0 ALPHA - 1 * 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 . ---------------------------------------------------------------- FOR EXPONENTS ( 2 ALPHA ) AND ( ALPHA - 1 ) OF g, WITH alpha = - 1 , POWER OF g is - 2 ----> SOLVE FOR U 0 1 TERM (U - 1) U -- IS DOMINANT 0 0 2 G IN EQUATION. ---------------------------------------------------------------- 1 ) WITH U = 1 ----> FIND RESONANCES 0 ALPHA R + ALPHA SUBSTITUTE U G + U G FOR f IN EQUATION 0 R R - 2 TERM ( R + 1 ) U G IS DOMINANT R IN EQUATION. THERE ARE NO NON-NEGATIVE INTEGRAL ROOTS FOR r. ---------------------------------------------------------------- (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 <= [0] 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() > ---------------------------------------------------------------- (C17) /* ************************** END of NP_EXEC.MAX ************************** */ (D17) DONE (C18) closefile();