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

Abstract

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.

References in corpus (5)

• Travelling waves for the Gross-Pitaevskii equation II
• Supercritical geometric optics for nonlinear Schrodinger equations
• Geometric optics and boundary layers for Nonlinear Schrodinger equations
• Existence of multi-solitons for the focusing Logarithmic Non-Linear Schrodinger Equation
• WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity