WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework
Analysis of PDEs
2021-09-13 v1
Abstract
We are interested in a WKB analysis of the Logarithmic Non-Linear Schr\"odinger 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 at infinity.
Keywords
Cite
@article{arxiv.2011.12198,
title = {WKB analysis of the Logarithmic Nonlinear Schrodinger Equation in an analytic framework},
author = {Guillaume Ferriere},
journal= {arXiv preprint arXiv:2011.12198},
year = {2021}
}