The Complex WKB Method for Nonlinear Equations I: Linear Theory - Couverture souple

Maslov, Victor P.

Couverture souple

ISBN 10 : 3034896697 ISBN 13 : 9783034896696

Editeur : Birkhäuser, 2012

Synopsis

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.

Détails de l'édition

• Éditeur: Birkhäuser
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 3034896697
• ISBN 13: 9783034896696
• Reliure: Broché
• Nombre de pages: 316
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible