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Overview"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." Full Product DetailsAuthor: Victor P. Maslov , M.A. Shishkova , A.B. Sossinsky , A. B. SossinskyPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: Softcover reprint of the original 1st ed. 1994 Volume: 16 Dimensions: Width: 15.50cm , Height: 1.60cm , Length: 23.50cm Weight: 0.486kg ISBN: 9783034896696ISBN 10: 3034896697 Pages: 304 Publication Date: 06 October 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |