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Semi-classical Analysis For Nonlinear Schrodinger Equations

Engelsk Hardback

Semi-classical Analysis For Nonlinear Schrodinger Equations

Engelsk Hardback

925 kr
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Om denne bog
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.
Product detaljer
Sprog:
Engelsk
Sider:
256
ISBN-13:
9789812793126
Indbinding:
Hardback
Udgave:
ISBN-10:
9812793127
Udg. Dato:
5 mar 2008
Længde:
19mm
Bredde:
162mm
Højde:
237mm
Forlag:
World Scientific Publishing Co Pte Ltd
Oplagsdato:
5 mar 2008
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