On the Generation of Dispersive Shock Waves

Peter D. Miller

doi:10.1016/j.physd.2016.04.011

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arXiv · 1510.03686

On the Generation of Dispersive Shock Waves

Peter D. Miller

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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.

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Peter D. Miller. 2015-10-13. On the Generation of Dispersive Shock Waves. https://doi.org/10.1016/j.physd.2016.04.011

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