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Semi-Classical Analysis For Nonlinear Schrodinger Equations [Hardcover]

By Rémi Carles (Author)
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Item description for Semi-Classical Analysis For Nonlinear Schrodinger Equations by Rémi Carles...

These lecture notes review recent results on the high-frequency analysis of nonlinear Schrdinger 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 Schrdinger 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.

Contents: WKB Analysis: Preliminary 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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Item Specifications...

Studio: World Scientific Publishing Company
Pages   256
Est. Packaging Dimensions:   Length: 8.98" Width: 6.14" Height: 0.79"
Weight:   1.1 lbs.
Binding  Hardcover
Release Date   Mar 4, 2008
Publisher   World Scientific Publishing Company
ISBN  9812793127  
ISBN13  9789812793126  

Availability  0 units.

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1Books > Subjects > Professional & Technical > Medical > Medicine > Surgery > Neurosurgery
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > Differential Equations
3Books > Subjects > Science > General
4Books > Subjects > Science > Mathematics > Applied > Differential Equations
5Books > Subjects > Science > Mathematics > General

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