Dynamic rescaling for tracking point singularities: application to Nonlinear Schrödinger equation and related problems

We present a method with which equations that develop a localized singu larity can be integrated numerically up to times very close to the singularity formation. We apply the method, which is based on a dynamic rescaling, to self-focusing solutions of the Nonlinear Schrodinger equation, the Zakharov equations for Langmuir waves in plasmas and the Davey Stewartson equation for capillary-gravity waves at a fluid surface.

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