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The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse

✍ Scribed by Catherine Sulem, Pierre-Louis Sulem

Publisher
Springer
Year
1999
Tongue
English
Leaves
369
Series
Applied Mathematical Sciences
Edition
1
Category
Library
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✦ Synopsis

This monograph aims to fill the gap between the mathematical literature which significantly contributed during the last decade to the understanding of the collapse phenomenon, and applications to domains like plasma physics and nonlinear optics where this process provides a fundamental mechanism for small scale formation and wave dissipation. This results in a localized heating of the medium and in the case of propagation in a dielectric to possible degradation of the material. For this purpose, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal asymptotic expansions and numerical simulations.

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