An Asymptotic Preserving Scheme Based on a New Formulation for NLS in the Semiclassical Limit
An Asymptotic Preserving Scheme Based on a New Formulation for NLS in the Semiclassical Limit
We consider the semiclassical limit for the nonlinear Schrodinger equation. We introduce a phase/amplitude representation given by a system similar to the hydrodynamical formulation, whose novelty consists in including some asymptotically vanishing viscosity. We prove that the system is always locally well-posed in a class of Sobolev spaces, and globally …