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portada The Complex Wkb Method for Nonlinear Equations I: Linear Theory
Type
Physical Book
Author
Translated by
Publisher
Language
English
Pages
304
Format
Paperback
Dimensions
23.4 x 15.6 x 1.7 cm
Weight
0.44 kg.
ISBN13
9783034896696
Categories

The Complex Wkb Method for Nonlinear Equations I: Linear Theory

Victor P. Maslov (Author) · A. B. Sossinsky (Translated by) · M. a. Shishkova (Translated by) · Birkhauser · Paperback

The Complex Wkb Method for Nonlinear Equations I: Linear Theory - Maslov, Victor P. ; Shishkova, M. a. ; Sossinsky, A. B.

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Synopsis "The Complex Wkb Method for Nonlinear Equations I: Linear Theory"

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.

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