The Complex WKB Method for Nonlinear Equations I: Linear Theory - Progress in Mathematical Physics - Victor P. Maslov - Livros - Springer Basel - 9783034896696 - 6 de outubro de 2012
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The Complex WKB Method for Nonlinear Equations I: Linear Theory - Progress in Mathematical Physics Softcover reprint of the original 1st ed. 1994 edition

Victor P. Maslov

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The Complex WKB Method for Nonlinear Equations I: Linear Theory - Progress in Mathematical Physics Softcover reprint of the original 1st ed. 1994 edition

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.


311 pages, 2 black & white illustrations

Mídia Livros     Paperback Book   (Livro de capa flexível e brochura)
Lançado 6 de outubro de 2012
Data do lançamento original 1994
ISBN13 9783034896696
Editoras Springer Basel
Páginas 304
Dimensões 155 × 235 × 16 mm   ·   444 g
Idioma English  
Tradutor Shishkova, M.A.
Tradutor Sossinsky, A.B.

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