Symmetry-adapted moving mesh schemes for the nonlinear Schrödinger equation

In this paper we consider symmetry-preserving difference schemes for the nonlinear Schrodinger equation where n is the number of space dimensions. This equation describes one-dimensional waves in n space dimensions in many physical situations, including phenomena in plasma physics and nonlinear optics. We will consider the nonintegrable case n≥2 for which the equation admits solutions that blow up in a finite time, and construct discretizations based upon moving mesh schemes that have the same Lie group properties and Lagrangian structures as the continuous counterpart.

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