Semi-classical analysis for nonlinear Schrödinger equations /:
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 construct...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; Hackensack, NJ :
World Scientific,
©2008.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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 resource (xi, 243 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 233-241) and index. |
| ISBN: | 9789812793133 9812793135 1281934216 9781281934215 9786611934217 6611934219 |
Internformat
MARC
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| 245 | 1 | 0 | |a Semi-classical analysis for nonlinear Schrödinger equations / |c Rémi Carles. |
| 260 | |a Singapore ; |a Hackensack, NJ : |b World Scientific, |c ©2008. | ||
| 300 | |a 1 online resource (xi, 243 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (pages 233-241) and index. | ||
| 505 | 0 | |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. | |
| 588 | 0 | |a Print version record. | |
| 520 | |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. | ||
| 546 | |a English. | ||
| 650 | 0 | |a Schrödinger equation. |0 http://id.loc.gov/authorities/subjects/sh85118495 | |
| 650 | 0 | |a Nonlinear theories. |0 http://id.loc.gov/authorities/subjects/sh85092332 | |
| 650 | 6 | |a Équation de Schrödinger. | |
| 650 | 6 | |a Théories non linéaires. | |
| 650 | 7 | |a SCIENCE |x Waves & Wave Mechanics. |2 bisacsh | |
| 650 | 7 | |a Nonlinear theories |2 fast | |
| 650 | 7 | |a Schrödinger equation |2 fast | |
| 758 | |i has work: |a Semi-classical analysis for nonlinear Schrödinger equations (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFyBKMXFRfrMYQ9xBrbVBX |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
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Datensatz im Suchindex
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| author | Carles, Rémi |
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| author_facet | Carles, Rémi |
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| callnumber-first | Q - Science |
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| contents | 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. |
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| dewey-ones | 530 - Physics |
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| discipline | Physik Mathematik |
| format | Electronic eBook |
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ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 233-241) and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="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.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="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. 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| id | ZDB-4-EBA-ocn560636924 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:01Z |
| institution | BVB |
| isbn | 9789812793133 9812793135 1281934216 9781281934215 9786611934217 6611934219 |
| language | English |
| oclc_num | 560636924 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 243 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Carles, Rémi. https://id.oclc.org/worldcat/entity/E39PCjBXPhPTbm4yBKGvDpgjbq http://id.loc.gov/authorities/names/no2008090154 Semi-classical analysis for nonlinear Schrödinger equations / Rémi Carles. Singapore ; Hackensack, NJ : World Scientific, ©2008. 1 online resource (xi, 243 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references (pages 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. Print version record. 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. English. Schrödinger equation. http://id.loc.gov/authorities/subjects/sh85118495 Nonlinear theories. http://id.loc.gov/authorities/subjects/sh85092332 Équation de Schrödinger. Théories non linéaires. SCIENCE Waves & Wave Mechanics. bisacsh Nonlinear theories fast Schrödinger equation fast has work: Semi-classical analysis for nonlinear Schrödinger equations (Text) https://id.oclc.org/worldcat/entity/E39PCFyBKMXFRfrMYQ9xBrbVBX https://id.oclc.org/worldcat/ontology/hasWork Print version: Carles, Rémi. Semi-classical analysis for nonlinear Schrödinger equations. Singapore ; Hackensack, NJ : World Scientific, ©2008 9812793127 9789812793126 (DLC) 2008297932 (OCoLC)198759348 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236100 Volltext |
| spellingShingle | Carles, Rémi Semi-classical analysis for nonlinear Schrödinger equations / 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. Schrödinger equation. http://id.loc.gov/authorities/subjects/sh85118495 Nonlinear theories. http://id.loc.gov/authorities/subjects/sh85092332 Équation de Schrödinger. Théories non linéaires. SCIENCE Waves & Wave Mechanics. bisacsh Nonlinear theories fast Schrödinger equation fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85118495 http://id.loc.gov/authorities/subjects/sh85092332 |
| 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 | Schrödinger equation. http://id.loc.gov/authorities/subjects/sh85118495 Nonlinear theories. http://id.loc.gov/authorities/subjects/sh85092332 Équation de Schrödinger. Théories non linéaires. SCIENCE Waves & Wave Mechanics. bisacsh Nonlinear theories fast Schrödinger equation fast |
| topic_facet | Schrödinger equation. Nonlinear theories. Équation de Schrödinger. Théories non linéaires. SCIENCE Waves & Wave Mechanics. Nonlinear theories Schrödinger equation |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=236100 |
| work_keys_str_mv | AT carlesremi semiclassicalanalysisfornonlinearschrodingerequations |