On the generation of dispersive shock waves

[摘要] 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. (C) 2016 Elsevier B.V. All rights reserved.

[发布日期] 2016-10-15

[效力级别]  Proceedings Paper

[关键词] Semiclassical limit;Small-dispersion limit;Lax-Levermore theory;Deift-Zhou steepest descent method;Universality