Hydrodynamics of modulated finite-amplitude waves in dispersive media

Analytic approaches are developed for integrating the nondiagonalizable Whi tham equations for the generation and propagation of nonlinear modulated fi nite-amplitude waves in dissipationless dispersive media. Natural matching conditions for these equations are stated in a general form analogous to th e Gurevich-Pitaevskii conditions for the averaged Korteweg-de Vries equatio ns. Exact relationships between the hydrodynamic quantities on different si des of a dissipationless shock wave, an analog of the shock adiabat in ordi nary dissipative hydrodynamics and first proposed on the basis of physical considerations by Gurevich and Meshcherkin,(4) are obtained. The boundaries of a self similar, dissipationless shock wave are determined analytically as a function of the density jump. Some specific examples are considered. ( C) 1999 American Institute of Physics. [S1063-7761(99)02603-7].