On the generation of dispersive shock waves

PHYSICA D-NONLINEAR PHENOMENA

卷:333

Article; Proceedings Paper

Miller, Peter D.¹ 

[1] Univ Michigan, Dept Math, East Hall,530 Church St, Ann Arbor, MI 48109 USA

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

DOI  :  10.1016/j.physd.2016.04.011

来源: Elsevier

【 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.

【 授权许可】

Free