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THREE LONG WAVE ASYMPTOTIC REGIMES FOR THE NONLINEAR-SCHRODINGER EQUATION. David CHIRON Laboratoire J.A. DIEUDONNE, Universite de Nice - Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France. Abstract. We survey some recent results related to three long wave asymptotic regimes for the Nonlinear-Schrodinger Equation: the Euler regime corresponding to the WKB method, the linear wave regime and finally the KdV/KP-I asymptotic dynamics. 1. Introduction The nonlinear Schrodinger equation (NLS) i∂?∂? + 1 2 ∆? = ?f(|?|2), ? : R+ ? Rd ? C appears as a relevant model in condensed matter physics: in nonlinear Optics (see, for instance, the survey [48]); in Bose-Einstein condensation and superfluidity (see [65], [29], [32], [1]). The nonlinearity f may be f(?) = ? or f(?) = ??1, in which case (NLS) is termed the Gross-Pitaevskii equation, or f(?) = ?2 (see, e.g., [50]) in the context of Bose-Einstein condensates, and more generally a pure power. In nonlinear Optics, quite often in dimensions 1 or 2, the nonlinearity may be more complicated (cf.

- equation satisfied
- free wave
- results related
- compressible euler
- asymptotic regime
- einstein condensation
- v? ·
- ??
- gross-pitaevskii equation
- euler system

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