| The Complex Wkb Method for Nonlinear Equations I: Linear Theory Softcover Repri Edition Contributor(s): Maslov, Victor P. (Author), Shishkova, M. a. (Translator), Sossinsky, A. B. (Translator) |
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ISBN: 3034896697 ISBN-13: 9783034896696 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: October 2012 |
| Additional Information |
| BISAC Categories: - Gardening - Science | Physics - Mathematical & Computational - Mathematics | Mathematical Analysis |
| Dewey: 515 |
| Series: Progress in Mathematical Physics |
| Physical Information: 0.66" H x 6.14" W x 9.21" (0.98 lbs) 304 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |
