An Asymptotically Preserving Approach for Nonlinear Schrödinger Equation in the Semiclassical Limit

Abstract

We study numerically the semiclassical limit for the nonlinear Schrödinger equation thanks to a modification of the Madelung transform due to E. Grenier. This approach is naturally asymptotically preserving, and allows for the presence of vacuum. Even if the mesh size and the time step do not depend on the Planck constant, we recover the position and… (More)

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