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Radiophysics and Quantum Electronics

, Volume 46, Issue 5–6, pp 307–322 | Cite as

Integral Criteria of Wave Collapses

  • E. A. Kuznetsov
Article

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.

Keywords

Dust Finite Time Gordon Equation Differential Inequality Landau Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • E. A. Kuznetsov
    • 1
  1. 1.L. D. Landau Institute of Theoretical Physics of the Russian Academy of SciencesMoscowRussia

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