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By O. Axelsson, L.S. Frank and A. Van Der Sluis (Eds.)

ISBN-10: 0080871585

ISBN-13: 9780080871585

ISBN-10: 0444861319

ISBN-13: 9780444861313

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Additional info for Analytical and Numerical Approaches to Asymptotic Problems in Analysis, Proceedings ofthe Conference on Analytical and Numerical Approachesto Asymptotic Problems

Example text

8 ) , k = 1. o e O L S u b s t i t u t i n g i n Q . [ y 1 and p , c y 1 t h e d e r i v a t i v e s S . and S , f o r U . ( E ) and V . ( E l , 3 0. 11, w e o b t a i n f o r E 0 , . . , E 2 e the required q u a s i - l i n e a r s y s t e m o f e q u a t i o n s . Note t h a t t h e i n t e g r a l s i n ( 6 . 6 ) can be w r i t t e n i n t h e form, which d o e s n o t r e q u i r e t h a t t h e p e r i o d s w i t h r e s p e c t t o t h e a r g u 2 ments ' T ~ , . . , T ~o f k-gap s o l u t i o n y o s h o u l d be e q u a l t o 2n.

Math. i Mech. 23, N3 (1959) 515-526 (in Russian). , A perturbation method for non-linear dispersive wave problems, Proc. ROY. SOC. A292, N 1430 (1966) 403-412. , Operational methods ("PTIR", Moscow, 1976). 1141 Maslov V . P . , Complex WKB-method in non-linear equations ("Nauka", Moscow, 1977) (in Russian). El51 Maslov V . P . , &-like generalized according to Sobolev solutions of quasi-linear equations, Uspekhi Math. Nauk 34, N1 (1979) 235-236 (in Russian). , Abelian functions and solutions, Inst.

3 ) and t h e f o r m u l a ( 5 . 4 ) . ,E2Y. ,E2e) H l l , . . ,Hg"p a n d C. This s o l u t i o n h a s t h e form C0 = a. P a . "O/aE. i n c a s e when a s t h e p a r a m e t e r s d e f i n i n g y t h e v a l u e s 3 3 E. a OP. a EZP. , II. jj and 8 . d e f i n e d a c c u r a t e t o a m u l t i p l i c a t i v e c o n s t a n t c a n be 3 3 o b t a i n e d from t h e s y s t e m o f e q u a t i o n s : The c o e f f i c i e n t s (1, i n t h e f i r s t c a s e and from i n t h e s e c o n d .

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Analytical and Numerical Approaches to Asymptotic Problems in Analysis, Proceedings ofthe Conference on Analytical and Numerical Approachesto Asymptotic Problems by O. Axelsson, L.S. Frank and A. Van Der Sluis (Eds.)


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