Geometric structure of 2D weak shock waves

摘要

A system of PDEs for two-dimensional weak shock waves (small amplitude) is obtained, which does not produce a caustic. A class of simple wave solutions and the complete class of separable solutions for these PDEs are given. Quasi-conservation-law forms and the related jump conditions together with their physical and geometrical aspects of these PDEs are discussed. The application to water waves is studied. Diffraction of the wave front around a convex wall using this theory is solved, and the results are compared with those given by Whitham and Lighthill.