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WKB Analysis for Nonlinear Schrödinger Equations with Potential

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Abstract

We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besides subquadratic potentials, we consider initial phases which may be unbounded. For this, we construct solutions for some compressible Euler equations with unbounded source term and unbounded initial velocity.

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  1. MAB, Université de Bordeaux 1, 351 cours de la Libération, 33405, Talence cedex, France

    Rémi Carles

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  1. Rémi Carles
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Correspondence to Rémi Carles.

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Communicated by P. Constantin

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Carles, R. WKB Analysis for Nonlinear Schrödinger Equations with Potential. Commun. Math. Phys. 269, 195–221 (2007). https://doi.org/10.1007/s00220-006-0077-2

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