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Article Dans Une Revue Communications in Contemporary Mathematics Année : 2021

WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework

Résumé

We are interested in a WKB analysis of the Logarithmic Non-Linear Schrödinger Equation with "Riemann-like" variables in an analytic framework in semiclassical regime. We show that the Cauchy problem is locally well posed uniformly in the semiclassical constant and that the semiclassical limit can be performed. In particular, our framework is not only compatible with the Gross-Pitaevskii equation with logarithmic nonlinearity, but also allows initial data (and solutions) which can converge to 0 at infinity.
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Dates et versions

hal-03022117 , version 1 (24-11-2020)

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Guillaume Ferriere. WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework. Communications in Contemporary Mathematics, 2021, ⟨10.1142/S0219199721500826⟩. ⟨hal-03022117⟩
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