On the Generation of Dispersive Shock Waves

Abstract

We review various methods for the analysis of initial-value problems for integrable dispersive equations in the weak-dispersion or semiclassical regime. Some methods are sufficiently powerful to rigorously explain the generation of modulated wavetrains, so-called dispersive shock waves, as the result of shock formation in a limiting dispersionless system. They also provide a detailed description of the solution near caustic curves that delimit dispersive shock waves, revealing fascinating universal wave patterns.

20 pages, 9 figures. Submitted to Physica D

References in corpus (4)

• Numerical Study of the semiclassical limit of the Davey-Stewartson II equations
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• Semiclassical soliton ensembles for the three-wave resonant interaction equations
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• Semiclassical soliton ensembles for the three-wave resonant interaction equations
• Nonlinear dispersive regularization of inviscid gas dynamics
• On nonlinear effects in multiphase WKB analysis for the nonlinear Schrodinger equation