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This paper has been published in Physica D. To download a preprint of this paper just click here.

This material is based upon work supported by the National Science Foundation under Grant No. DMS-1513054. Any opinions, findings and conclusions or recomendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation (NSF).

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On the Generation of Dispersive Shock Waves

Peter D. Miller

Department of Mathematics, University of Michigan, Ann Arbor


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.