Radiophysics and Quantum Electronics

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

Integral Criteria of Wave Collapses

  • E. A. Kuznetsov


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.


Dust Finite Time Gordon Equation Differential Inequality Landau Equation 
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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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