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Semi-Classical Analysis for Nonlinear Schrodinger Equations by Remi Carles

Semi-Classical Analysis for Nonlinear Schrodinger Equations

by Remi Carles
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Book cover type: Hardcover
  • ISBN13: 9789812793126
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: World Scientific Publishing Company
  • Publisher Imprint: World Scientific Publishing Company
  • Publication Date:
  • Pages: 256
  • Original Price: GBP 85.0
  • Language: English
  • Edition: N/A
  • Item Weight: 454 grams
  • BISAC Subject(s): Waves & Wave Mechanics

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.

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