Semi-classical Analysis For Nonlinear Schrodinger Equations
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A01=Remi Carles
Author_Remi Carles
Category=PBKD
Caustic
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Euler Equation
Hyperbolic Equations
Nonlinear SchrAfA?dinger Equation
Nonlinear Schrodinger Equation
Nonlinear Schrödinger Equation
Phase-Amplitude Representation
Scattering Theory
Semi-classical Limit
WKB Analysis
Product details
- ISBN 9789812793126
- Publication Date: 05 Mar 2008
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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 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.
