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 (15)

• Logarithmic nonlinearity in theories of quantum gravity: Origin of time and observational consequences
• Travelling waves for the Gross-Pitaevskii equation II
• Madelung, Gross-Pitaevskii and Korteweg
• Universal dynamics for the defocusing logarithmic Schrodinger equation
• On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations
• WKB analysis for nonlinear Schrödinger equations with potential
• 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
• The focusing logarithmic Schrödinger equation: analysis of breathers and nonlinear superposition
• Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations
• WKB analysis for the Gross-Pitaevskii equation with non-trivial boundary conditions at infinity
• Convergence rate in Wasserstein distance and semiclassical limit for the defocusing logarithmic Schr{ö}dinger equation
• Monokinetic solutions to a singular Vlasov equation from a semiclassical perspective
• WKB analysis of generalized derivative nonlinear Schrodinger equations without hyperbolicity