Semi-classical analysis for nonlinear Schrödinger equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2008
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 233-241) and index WKB analysis -- Weak nonlinear geometric optics -- Convergence of quadratic observables via modulated energy functionals -- Pointwise description of the wave function -- Some instability phenomena -- Caustic crossing : the case of focal points -- Caustic crossing : formal analysis -- Focal point without external potential -- Focal point in the presence of an external potential -- Some ideas for supercritical cases These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger e |
| Beschreibung: | 1 Online-Ressource (xi, 243 p.) |
| ISBN: | 9789812793126 9789812793133 9812793127 9812793135 |
Internformat
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| 500 | |a Includes bibliographical references (p. 233-241) and index | ||
| 500 | |a WKB analysis -- Weak nonlinear geometric optics -- Convergence of quadratic observables via modulated energy functionals -- Pointwise description of the wave function -- Some instability phenomena -- Caustic crossing : the case of focal points -- Caustic crossing : formal analysis -- Focal point without external potential -- Focal point in the presence of an external potential -- Some ideas for supercritical cases | ||
| 500 | |a These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger e | ||
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Datensatz im Suchindex
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| author | Carles, Rémi |
| author_facet | Carles, Rémi |
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| author_sort | Carles, Rémi |
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| bvnumber | BV043116986 |
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| ctrlnum | (OCoLC)560636924 (DE-599)BVBBV043116986 |
| dewey-full | 530.12/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.12/4 |
| dewey-search | 530.12/4 |
| dewey-sort | 3530.12 14 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV043116986 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:17:57Z |
| institution | BVB |
| isbn | 9789812793126 9789812793133 9812793127 9812793135 |
| language | English |
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| oclc_num | 560636924 |
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| physical | 1 Online-Ressource (xi, 243 p.) |
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| spelling | Carles, Rémi Verfasser aut Semi-classical analysis for nonlinear Schrödinger equations Rémi Carles Singapore World Scientific c2008 1 Online-Ressource (xi, 243 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 233-241) and index WKB analysis -- Weak nonlinear geometric optics -- Convergence of quadratic observables via modulated energy functionals -- Pointwise description of the wave function -- Some instability phenomena -- Caustic crossing : the case of focal points -- Caustic crossing : formal analysis -- Focal point without external potential -- Focal point in the presence of an external potential -- Some ideas for supercritical cases These lecture notes review recent results on the high-frequency analysis of nonlinear Schrödinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrödinger e SCIENCE / Waves & Wave Mechanics bisacsh Nonlinear theories fast Schrödinger equation fast Schrödinger equation Nonlinear theories WKB-Methode (DE-588)4190133-2 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd rswk-swf Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 s WKB-Methode (DE-588)4190133-2 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=236100 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Carles, Rémi Semi-classical analysis for nonlinear Schrödinger equations SCIENCE / Waves & Wave Mechanics bisacsh Nonlinear theories fast Schrödinger equation fast Schrödinger equation Nonlinear theories WKB-Methode (DE-588)4190133-2 gnd Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd |
| subject_GND | (DE-588)4190133-2 (DE-588)4278277-6 |
| title | Semi-classical analysis for nonlinear Schrödinger equations |
| title_auth | Semi-classical analysis for nonlinear Schrödinger equations |
| title_exact_search | Semi-classical analysis for nonlinear Schrödinger equations |
| title_full | Semi-classical analysis for nonlinear Schrödinger equations Rémi Carles |
| title_fullStr | Semi-classical analysis for nonlinear Schrödinger equations Rémi Carles |
| title_full_unstemmed | Semi-classical analysis for nonlinear Schrödinger equations Rémi Carles |
| title_short | Semi-classical analysis for nonlinear Schrödinger equations |
| title_sort | semi classical analysis for nonlinear schrodinger equations |
| topic | SCIENCE / Waves & Wave Mechanics bisacsh Nonlinear theories fast Schrödinger equation fast Schrödinger equation Nonlinear theories WKB-Methode (DE-588)4190133-2 gnd Nichtlineare Schrödinger-Gleichung (DE-588)4278277-6 gnd |
| topic_facet | SCIENCE / Waves & Wave Mechanics Nonlinear theories Schrödinger equation WKB-Methode Nichtlineare Schrödinger-Gleichung |
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