A numerical study of the semi-classical limit of the focusing nonlinear Schrödinger equation

A Semi-implicit Moving Mesh Method for the Focusing Nonlinear Schrödinger Equation

An efficient adaptive moving mesh method for investigation of the semi-classical limit of the focusing nonlinear Schrödinger equation is presented. The method employs a dynamic mesh to resolve the sea of solitons observed for small dispersion parameters. A second order semi-implicit discretization is used in conjunction with a dynamic mesh generator to achieve a cost-efficient, accurate, and st...

On the Semi-classical Limit for the Nonlinear Schrödinger Equation

We review some results concerning the semi-classical limit for the nonlinear Schrödinger equation, with or without an external potential. We consider initial data which are either of the WKB type, or very concentrated as the semi-classical parameter goes to zero. We sketch the techniques used according to various frameworks, and point out some open problems.

Semiclassical Limit of the Nonlinear Schrödinger-Poisson Equation with Subcritical Initial Data

We study the semi-classical limit of the nonlinear Schrödinger-Poisson (NLSP) equation for initial data of the WKB type. The semi-classical limit in this case is realized in terms of a density-velocity pair governed by the Euler-Poisson equations. Recently we have shown in [ELT, Indiana Univ. Math. J., 50 (2001), 109–157], that the isotropic Euler-Poisson equations admit a critical threshold ph...

On the semi-classical limit for the focusing nonlinear Schrodinger equation: sensitivity to analytic properties of the initial data

We present the results of a large number of careful numerical experiments carried out to investigate the way that the solution of the integrable focusing nonlinear Schrodinger equation with ­ xed initial data, when taken to be close to the semiclassical limit, depends on analyticity properties of the data. In particular, we study a family of initial data that have complex singularities at an a...

Existence and Semi–Classical Limit of the Least Energy Solution to a Nonlinear Schrödinger Equation with Electromagnetic Fields