Rank-κ solutions of hydrodynamic-type systems

A. M. Grundland; B. Huard

doi:10.1007/s11232-007-0080-6

Rank-κ solutions of hydrodynamic-type systems

A. M. Grundland^*, B. Huard

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	948-962
Number of pages	15
Journal	Theoretical and Mathematical Physics
Volume	152
Issue number	1
DOIs	https://doi.org/10.1007/s11232-007-0080-6
Publication status	Published - 1 Jul 2007
Externally published	Yes

Keywords

Conditional symmetry
Rank-k solution of partial differential equations
Riemann invariant

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10.1007/s11232-007-0080-6

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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).",

keywords = "Conditional symmetry, Rank-k solution of partial differential equations, Riemann invariant",

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Y1 - 2007/7/1

N2 - 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).

AB - 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).

KW - Conditional symmetry

KW - Rank-k solution of partial differential equations

KW - Riemann invariant

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JO - Theoretical and Mathematical Physics

JF - Theoretical and Mathematical Physics

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Rank-κ solutions of hydrodynamic-type systems

Abstract

Keywords

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