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Numerical study of the logarithmic Schrodinger equation with repulsive harmonic potential
Remi Carles, Chunmei Su
We consider the Schrodinger equation with a logarithmic nonlinearity and a repulsive harmonic potential. Depending on the parameters of the equation, the solution may or may not be…
Error estimates of local energy regularization for the logarithmic Schrodinger equation
Weizhu Bao, Remi Carles, Chunmei Su +1
The logarithmic nonlinearity has been used in many partial differential equations (PDEs) for modeling problems in various applications.Due to the singularity of the logarithmic fun…
Regularized numerical methods for the logarithmic Schrodinger equation
Weizhu Bao, Rémi Carles, Chunmei Su +1
We present and analyze two numerical methods for the logarithmic Schr{ö}dinger equation (LogSE) consisting of a regularized splitting method and a regularized conservative Crank-Ni…
Error estimates of a regularized finite difference method for the logarithmic Schrödinger equation
Weizhu Bao, Remi Carles, Chunmei Su +1
We present a regularized finite difference method for the logarithmic Schrödinger equation (LogSE) and establish its error bound. Due to the blow-up of the logarithmic nonlinearity…
On Fourier time-splitting methods for nonlinear Schrodinger equations in the semi-classical limit II. Analytic regularity
Rémi Carles, Clément Gallo
We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrodinger equation, in the semi-classical limit, with initial data under the form of WKB sta…
An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
Christophe Besse, Rémi Carles, Florian Méhats
We consider the semiclassical limit for the nonlinear Schrodinger equation. We introduce a phase/amplitude representation given by a system similar to the hydrodynamical formulatio…