The Complex WKB Method for Nonlinear Equations I.

Victor P. Maslov

ISBN 10: 3764350881 ISBN 13: 9783764350888

Published by Birkhauser, 1994

Language: English

Condition: Used Hardcover

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Bibliographic Details

Title

The Complex WKB Method for Nonlinear Equations I.

Publisher

Birkhauser

Publication Date

1994

Language

English

ISBN 10

3764350881

ISBN 13

9783764350888

Binding

Hardcover

Condition

Very god

Dust Jacket Condition

No jacket

Seller catalogs

About this title

Synopsis

This book deals with asymptotic solutions of linear and nonlinear equa- tions which decay as h ---] 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp- totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob- lems of mathematical physics; certain specific formulas were obtained by differ- ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter- nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: "One can hope that in the near future a computational pro- cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.

Language Notes

Text: English
Original Language: Russian

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