Singular Limits of Dispersive Waves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Springer US
1994
|
| Schriftenreihe: | NATO ASI Series, Series B: Physics
320 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The subject, of "Singular Limits of Dispersive vVaves" had its modern origins in the 1960's when Whitham introduced the first systematic approach to the asymptotic analysis of nonlinear wavepackds. Initially developed through a variational principle applied to the modulation of families of traveling wave solutions, he soon realized that an efficient derivation of modulation eq'uations could b(' accomplished by av eraging local conservation laws. He carried out this analysis for a wide variety of dispersive nonlinear wave equations including the nonlinear Klein Gordon, KdV, and NLS equations. The seminal work of Gardner, Greene, Kruskal and Miura led to the discovery of partial differential equations which are completely integrable through inverse spectral transforms. This provided a larger framework in which to develop modulation theory. In particular, one could consider the local modulation of families of quasiperiodic so lutions with an arbitrary number ofphases. extending the sillglf' phase traveling waves treated Ly \Vhitham. The first to extend vVhitham's ideas to the mllltiphase setting were Flaschka, Forest and lvIcLaughlin, who derived N-phase modulation equations for the KdV equation. By using geometric techniques from the theory of Riemann surfaces they presented these equations in Riemann invariant form and demonstrated their hyperbolicity |
| Beschreibung: | 1 Online-Ressource (XIV, 369 p) |
| ISBN: | 9781461524748 9781461360544 |
| ISSN: | 0258-1221 |
| DOI: | 10.1007/978-1-4615-2474-8 |
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| 245 | 1 | 0 | |a Singular Limits of Dispersive Waves |c edited by N. M. Ercolani, I. R. Gabitov, C. D. Levermore, D. Serre |
| 246 | 1 | 3 | |a Proceedings of a NATO ARW and of a Chaos, Order, and Patterns Panel sponsored workshop held in Lyons, France, July 8-12, 1991 |
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| 500 | |a The subject, of "Singular Limits of Dispersive vVaves" had its modern origins in the 1960's when Whitham introduced the first systematic approach to the asymptotic analysis of nonlinear wavepackds. Initially developed through a variational principle applied to the modulation of families of traveling wave solutions, he soon realized that an efficient derivation of modulation eq'uations could b(' accomplished by av eraging local conservation laws. He carried out this analysis for a wide variety of dispersive nonlinear wave equations including the nonlinear Klein Gordon, KdV, and NLS equations. The seminal work of Gardner, Greene, Kruskal and Miura led to the discovery of partial differential equations which are completely integrable through inverse spectral transforms. This provided a larger framework in which to develop modulation theory. In particular, one could consider the local modulation of families of quasiperiodic so lutions with an arbitrary number ofphases. extending the sillglf' phase traveling waves treated Ly \Vhitham. The first to extend vVhitham's ideas to the mllltiphase setting were Flaschka, Forest and lvIcLaughlin, who derived N-phase modulation equations for the KdV equation. By using geometric techniques from the theory of Riemann surfaces they presented these equations in Riemann invariant form and demonstrated their hyperbolicity | ||
| 650 | 4 | |a Physics | |
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| 700 | 1 | |a Gabitov, I. R. |e Sonstige |4 oth | |
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| 700 | 1 | |a Serre, D. |e Sonstige |4 oth | |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
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| discipline | Physik |
| doi_str_mv | 10.1007/978-1-4615-2474-8 |
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| id | DE-604.BV042411565 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:20:48Z |
| institution | BVB |
| isbn | 9781461524748 9781461360544 |
| issn | 0258-1221 |
| language | English |
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| spelling | Ercolani, N. M. Verfasser aut Singular Limits of Dispersive Waves edited by N. M. Ercolani, I. R. Gabitov, C. D. Levermore, D. Serre Proceedings of a NATO ARW and of a Chaos, Order, and Patterns Panel sponsored workshop held in Lyons, France, July 8-12, 1991 Boston, MA Springer US 1994 1 Online-Ressource (XIV, 369 p) txt rdacontent c rdamedia cr rdacarrier NATO ASI Series, Series B: Physics 320 0258-1221 The subject, of "Singular Limits of Dispersive vVaves" had its modern origins in the 1960's when Whitham introduced the first systematic approach to the asymptotic analysis of nonlinear wavepackds. Initially developed through a variational principle applied to the modulation of families of traveling wave solutions, he soon realized that an efficient derivation of modulation eq'uations could b(' accomplished by av eraging local conservation laws. He carried out this analysis for a wide variety of dispersive nonlinear wave equations including the nonlinear Klein Gordon, KdV, and NLS equations. The seminal work of Gardner, Greene, Kruskal and Miura led to the discovery of partial differential equations which are completely integrable through inverse spectral transforms. This provided a larger framework in which to develop modulation theory. In particular, one could consider the local modulation of families of quasiperiodic so lutions with an arbitrary number ofphases. extending the sillglf' phase traveling waves treated Ly \Vhitham. The first to extend vVhitham's ideas to the mllltiphase setting were Flaschka, Forest and lvIcLaughlin, who derived N-phase modulation equations for the KdV equation. By using geometric techniques from the theory of Riemann surfaces they presented these equations in Riemann invariant form and demonstrated their hyperbolicity Physics Theoretical, Mathematical and Computational Physics Gabitov, I. R. Sonstige oth Levermore, C. D. Sonstige oth Serre, D. Sonstige oth https://doi.org/10.1007/978-1-4615-2474-8 Verlag Volltext |
| spellingShingle | Ercolani, N. M. Singular Limits of Dispersive Waves Physics Theoretical, Mathematical and Computational Physics |
| title | Singular Limits of Dispersive Waves |
| title_alt | Proceedings of a NATO ARW and of a Chaos, Order, and Patterns Panel sponsored workshop held in Lyons, France, July 8-12, 1991 |
| title_auth | Singular Limits of Dispersive Waves |
| title_exact_search | Singular Limits of Dispersive Waves |
| title_full | Singular Limits of Dispersive Waves edited by N. M. Ercolani, I. R. Gabitov, C. D. Levermore, D. Serre |
| title_fullStr | Singular Limits of Dispersive Waves edited by N. M. Ercolani, I. R. Gabitov, C. D. Levermore, D. Serre |
| title_full_unstemmed | Singular Limits of Dispersive Waves edited by N. M. Ercolani, I. R. Gabitov, C. D. Levermore, D. Serre |
| title_short | Singular Limits of Dispersive Waves |
| title_sort | singular limits of dispersive waves |
| topic | Physics Theoretical, Mathematical and Computational Physics |
| topic_facet | Physics Theoretical, Mathematical and Computational Physics |
| url | https://doi.org/10.1007/978-1-4615-2474-8 |
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