Hydrodynamics of modulated finite-amplitude waves in dispersive media

A. V. Tyurina*, G. A. Él'

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


Analytic approaches are developed for integrating the nondiagonalizable Whitham equations for the generation and propagation of nonlinear modulated finite-amplitude waves in dissipationless dispersive media. Natural matching conditions for these equations are stated in a general form analogous to the Gurevich-Pitaevskii conditions for the averaged Kortewegde Vries equations. Exact relationships between the hydrodynamic quantities on different sides of a dissipationless shock wave, an analog of the shock adiabat in ordinary 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.

Original languageEnglish
Pages (from-to)615-625
Number of pages11
JournalJournal of Experimental and Theoretical Physics
Issue number3
Publication statusPublished - Mar 1999
Externally publishedYes


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