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Global dynamics above the ground state energy for the combined power-type nonlinear schrödinger equations with energy-critical growth at low frequencies
Authors: --- --- ---
ISBN: 9781470448721 Year: 2021 Publisher: Providence : American Mathematical Society,

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Book
Extended states for the Schrödinger operator with quasi-periodic potential in dimension two
Authors: ---
ISBN: 9781470435431 1470435438 Year: 2019 Publisher: Providence, RI : American Mathematical Society,


Book
The Schrödinger model for the minimal representation of the indefinite orthogonal group O(p, q)
Authors: ---
ISBN: 9780821847572 Year: 2011 Volume: no. 1000 Publisher: Providence, R.I. American Mathematical Society

Hyperbolic equations and frequency interactions
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ISBN: 0821805924 9780821805923 Year: 1999 Volume: v. 5 Publisher: Providence (R.I.): American mathematical society,

The nonlinear Schrödinger equation : self-focusing and wave collapse
Authors: ---
ISBN: 0387986111 9786610145737 1280145730 0387227687 Year: 1999 Volume: 139 Publisher: New York : Springer,

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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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