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The Complex WKB Method for Nonlinear Equations I - Linear Theory (Paperback, Softcover reprint of the original 1st ed. 1994) Loot Price: R1,528
Discovery Miles 15 280
The Complex WKB Method for Nonlinear Equations I - Linear Theory (Paperback, Softcover reprint of the original 1st ed. 1994):...

The Complex WKB Method for Nonlinear Equations I - Linear Theory (Paperback, Softcover reprint of the original 1st ed. 1994)

Victor P. Maslov; Translated by M.A. Shishkova, A.B. Sossinsky

Series: Progress in Mathematical Physics, 16

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Loot Price R1,528 Discovery Miles 15 280 | Repayment Terms: R143 pm x 12*

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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: October 2012
First published: October 2012
Authors: Victor P. Maslov
Translators: M.A. Shishkova • A.B. Sossinsky
Dimensions: 235 x 155 x 16mm (L x W x T)
Format: Paperback
Pages: 304
Edition: Softcover reprint of the original 1st ed. 1994
ISBN-13: 978-3-03-489669-6
Categories: Books > Science & Mathematics > Physics > General
Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
Books > Science & Mathematics > Mathematics > Applied mathematics > General
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LSN: 3-03-489669-7
Barcode: 9783034896696

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