Semi-classical analysis for nonlinear Schrodinger equations:
These lecture notes review recent results on the high-frequency analysis of nonlinear Schrodinger 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...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2008
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| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | These lecture notes review recent results on the high-frequency analysis of nonlinear Schrodinger 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 Schrodinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated. These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided |
| Beschreibung: | xi, 243 p. ill |
| ISBN: | 9812793135 9789812793133 |
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| 520 | |a These lecture notes review recent results on the high-frequency analysis of nonlinear Schrodinger 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 Schrodinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated. These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided | ||
| 650 | 4 | |a Schrodinger equation | |
| 650 | 4 | |a Nonlinear theories | |
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| author | Carles, Remi |
| author_facet | Carles, Remi |
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| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV044635529 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:47Z |
| institution | BVB |
| isbn | 9812793135 9789812793133 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030033501 |
| oclc_num | 1012657488 |
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| physical | xi, 243 p. ill |
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| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | World Scientific Pub. Co. |
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| spelling | Carles, Remi Verfasser aut Semi-classical analysis for nonlinear Schrodinger equations Remi Carles Singapore World Scientific Pub. Co. c2008 xi, 243 p. ill txt rdacontent c rdamedia cr rdacarrier These lecture notes review recent results on the high-frequency analysis of nonlinear Schrodinger 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 Schrodinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated. These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided Schrodinger equation Nonlinear theories http://www.worldscientific.com/worldscibooks/10.1142/6753#t=toc Verlag URL des Erstveroeffentlichers Volltext |
| spellingShingle | Carles, Remi Semi-classical analysis for nonlinear Schrodinger equations Schrodinger equation Nonlinear theories |
| title | Semi-classical analysis for nonlinear Schrodinger equations |
| title_auth | Semi-classical analysis for nonlinear Schrodinger equations |
| title_exact_search | Semi-classical analysis for nonlinear Schrodinger equations |
| title_full | Semi-classical analysis for nonlinear Schrodinger equations Remi Carles |
| title_fullStr | Semi-classical analysis for nonlinear Schrodinger equations Remi Carles |
| title_full_unstemmed | Semi-classical analysis for nonlinear Schrodinger equations Remi Carles |
| title_short | Semi-classical analysis for nonlinear Schrodinger equations |
| title_sort | semi classical analysis for nonlinear schrodinger equations |
| topic | Schrodinger equation Nonlinear theories |
| topic_facet | Schrodinger equation Nonlinear theories |
| url | http://www.worldscientific.com/worldscibooks/10.1142/6753#t=toc |
| work_keys_str_mv | AT carlesremi semiclassicalanalysisfornonlinearschrodingerequations |