Rank-κ solutions of hydrodynamic-type systems

A. M. Grundland*, B. Huard

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We present a variant of the conditional symmetry method for obtaining rank-k solutions in terms of Riemann invariants for first-order quasilinear hyperbolic systems of PDEs in many dimensions and discuss examples of applying the proposed approach to fluid dynamics equations in n+1 dimensions in detail. We obtain several new types of algebraic, rational, and soliton-like solutions (including kinks, bumps, and multiple-wave solutions).

Original languageEnglish
Pages (from-to)948-962
Number of pages15
JournalTheoretical and Mathematical Physics
Volume152
Issue number1
DOIs
Publication statusPublished - 1 Jul 2007
Externally publishedYes

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