The Complex WKB Method for Nonlinear Equations I - Linear Theory (Hardcover, 1994 ed.)

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.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Progress in Mathematical Physics, 16
Release date:	August 1994
First published:	1994
Authors:	Victor P. Maslov
Translators:	M.A. Shishkova • A.B. Sossinsky
Dimensions:	235 x 155 x 25mm (L x W x T)
Format:	Hardcover
Pages:	304
Edition:	1994 ed.
ISBN-13:	978-3-7643-5088-8
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Complex analysis Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Geometry > General Books > Science & Mathematics > Mathematics > Topology > General Books > Science & Mathematics > Mathematics > Applied mathematics > General
LSN:	3-7643-5088-1
Barcode:	9783764350888

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