Science/Engineering Semi-Classical Analysis For Nonlinear Schrodinger Equations (repost) (9812793127)

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Semi-Classical Analysis For Nonlinear Schrodinger Equations

These lecture notes review recent results on the high-frequency analysis of nonlinear Schredinger 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 Schredinger 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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	Science/Engineering Semi-Classical Analysis For Nonlinear Schrodinger Equations Remi Carles “Semi-Classical Analysis For Nonlinear Schrodinger Equations" World Scientific Publishing Company \| 2008-03-04 \| ISBN: 9812793127 \| 256 pages \| PDF \| 2,6 MB These lecture notes review recent results on the high-frequenc ...
	Science/Engineering Global Solutions of Nonlinear Schrodinger Equations Global Solutions of Nonlinear Schrodinger Equations (Colloquium Publications (Amer Mathematical Soc)): Jean Bourgain American Mathematical Society \| ISBN: 0821819194 \| May 1999 \| djvu (ocr) \| 182 pages \| 3304 KB This volume presents recent ...
	Study The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives Panayotis G. Kevrekidis "The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives"Springer \| English \| 2009-07-14 \| ISBN: 3540891986 \| 415 pages \| PDF \| 12 MBThis book constitute ...
	The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computa The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives Free eBook download. Springer \| English \| 2009-07-14 \| ISBN: 3540891986 \| 415 pages \| PDF \| 12 MB This book c ...
	Technical Phase Space Analysis of Partial Differential Equations (Progress in Nonlinear Differential Equations and Their Applications) ISBN: 081764511X Publisher: BirkhÃ¤user Boston Author: Description:This collection of original articles and surveys treats the linear and nonlinear aspects of the theory of partial differential equations. Phase space analysis methods, inc ...
	Mathematics Contributions to Nonlinear Analysis: A Tribute to D.G. de Figueiredo on the Occasion of his 70th Birthday (Progress in Nonlinear Differential Equations and Their Applications) Author: Publisher: Birkhauser (2005)Binding: Hardcover, 518 pagespricer: $179.00ISBN-10: 3764371498editorialreviewsThis volume contains research and survey articles in the fields of nonlinear analysis and nonlinear differential equations, w ...

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