The Complex Wkb Method For Nonlinear Equations I: Linear Theory (Progress In Mathematical Physics) (V. 1)

The Complex Wkb Method For Nonlinear Equations I: Linear Theory (Progress In Mathematical Physics) (V. 1)

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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.

    Author

    Victor P. Maslov

    Binding

    Hardcover

    Creator

    M.A. Shishkova

    Creator

    A.B. Sossinsky

    EAN

    9783764350888

    Edition

    1994

    ISBN

    3764350881

    Label

    Birkhäuser

    Manufacturer

    Birkhäuser

    NumberOfPages

    304

    ProductGroup

    Book

    ProductTypeName

    ABIS_BOOK

    PublicationDate

    1994-08-01

    Publisher

    Birkhäuser

    Studio

    Birkhäuser

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