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Integral Criteria of Wave Collapses

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Radiophysics and Quantum Electronics Aims and scope

Abstract

We present an overview of the results of analysis of the integral criteria of wave collapses, i.e., the sufficient criteria of the formation of singularities from initially smooth wave-field distributions in a finite time. All such criteria are based on solving a majorizing second-order differential inequality which can be obtained for a wide range of models, including the nonlinear Schröodinger equation, the nonlinear Klein–Gordon equation, the time-dependent Ginzburg–Landau equation, the equations of dust hydrodynamics, the (Boussinesq) equation of a nonlinear string, and the generalized Kadomtsev–Petviashvili equation.

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  1. L. D. Landau Institute of Theoretical Physics of the Russian Academy of Sciences, Moscow, Russia

    E. A. Kuznetsov

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Kuznetsov, E.A. Integral Criteria of Wave Collapses. Radiophysics and Quantum Electronics 46, 307–322 (2003). https://doi.org/10.1023/A:1026355431307

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