Communications in Mathematical Physics

, Volume 160, Issue 1, pp 173–215 | Cite as

Existence of self-similar blow-up solutions for Zakhrov equation in dimension two. Part I

  • L. Glangetas
  • F. Merle
Article

Abstract

We consider the Zakharov equation in space dimension two
$$\left\{ {\begin{array}{*{20}c} {iu_t = - \Delta u + nu,} \\ {\frac{1}{{c_0^2 }}n_{tt} = \Delta n + \Delta \left| u \right|^2 } \\ \end{array} } \right.$$
. We prove the existence of blow-up solutions (stable “self-similar” blow-up solutions) for this problem and we study various properties of these solutions.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • L. Glangetas
    • 1
  • F. Merle
    • 2
  1. 1.Laboratoire d'Analyse NumériqueUniversité Pierre et Marie CurieParis Cedex 05France
  2. 2.Centre de MathématiquesUniversié de cergy-PontoisePontoise CedexFrance

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