The Complex WKB Method for Nonlinear Equations I: Linear Theory
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1994
|
| Schriftenreihe: | Progress in Physics
16 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book deals with asymptotic solutions of linear and nonlinear equations 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 asymptotics 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 problems of mathematical physics; certain specific formulas were obtained by different methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ternov [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 procedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed |
| Beschreibung: | 1 Online-Ressource (VII, 304 p) |
| ISBN: | 9783034885362 9783034896696 |
| DOI: | 10.1007/978-3-0348-8536-2 |
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| 100 | 1 | |a Maslov, Victor P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The Complex WKB Method for Nonlinear Equations I |b Linear Theory |c by Victor P. Maslov |
| 264 | 1 | |a Basel |b Birkhäuser Basel |c 1994 | |
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| 490 | 1 | |a Progress in Physics |v 16 | |
| 500 | |a This book deals with asymptotic solutions of linear and nonlinear equations 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 asymptotics 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 problems of mathematical physics; certain specific formulas were obtained by different methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ternov [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 procedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed | ||
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Datensatz im Suchindex
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| discipline | Physik Mathematik |
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| id | DE-604.BV042422156 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034885362 9783034896696 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857573 |
| oclc_num | 863674220 |
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| physical | 1 Online-Ressource (VII, 304 p) |
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| publisher | Birkhäuser Basel |
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| series | Progress in Physics |
| series2 | Progress in Physics |
| spelling | Maslov, Victor P. Verfasser aut The Complex WKB Method for Nonlinear Equations I Linear Theory by Victor P. Maslov Basel Birkhäuser Basel 1994 1 Online-Ressource (VII, 304 p) txt rdacontent c rdamedia cr rdacarrier Progress in Physics 16 This book deals with asymptotic solutions of linear and nonlinear equations 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 asymptotics 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 problems of mathematical physics; certain specific formulas were obtained by different methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ternov [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 procedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed Physics Global analysis (Mathematics) Theoretical, Mathematical and Computational Physics Analysis Progress in Physics 16 (DE-604)BV000002074 16 https://doi.org/10.1007/978-3-0348-8536-2 Verlag Volltext |
| spellingShingle | Maslov, Victor P. The Complex WKB Method for Nonlinear Equations I Linear Theory Progress in Physics Physics Global analysis (Mathematics) Theoretical, Mathematical and Computational Physics Analysis |
| title | The Complex WKB Method for Nonlinear Equations I Linear Theory |
| title_auth | The Complex WKB Method for Nonlinear Equations I Linear Theory |
| title_exact_search | The Complex WKB Method for Nonlinear Equations I Linear Theory |
| title_full | The Complex WKB Method for Nonlinear Equations I Linear Theory by Victor P. Maslov |
| title_fullStr | The Complex WKB Method for Nonlinear Equations I Linear Theory by Victor P. Maslov |
| title_full_unstemmed | The Complex WKB Method for Nonlinear Equations I Linear Theory by Victor P. Maslov |
| title_short | The Complex WKB Method for Nonlinear Equations I |
| title_sort | the complex wkb method for nonlinear equations i linear theory |
| title_sub | Linear Theory |
| topic | Physics Global analysis (Mathematics) Theoretical, Mathematical and Computational Physics Analysis |
| topic_facet | Physics Global analysis (Mathematics) Theoretical, Mathematical and Computational Physics Analysis |
| url | https://doi.org/10.1007/978-3-0348-8536-2 |
| volume_link | (DE-604)BV000002074 |
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