Elliptic solutions of isentropic ideal compressible fluid flow in (3 + 1) dimensions

Conte, Robert, Grundland, A. Michel and Huard, Benoit (2009) Elliptic solutions of isentropic ideal compressible fluid flow in (3 + 1) dimensions. Journal of Physics A: Mathematical and Theoretical, 42 (13). p. 135203. ISSN 1751-8113

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Official URL: http://dx.doi.org/10.1088/1751-8113/42/13/135203


A modified version of the conditional symmetry method, together with the classical method, is used to obtain new classes of elliptic solutions of the isentropic ideal compressible fluid flow in (3+1) dimensions. We focus on those types of solutions which are expressed in terms of the Weierstrass P-functions of Riemann invariants. These solutions are of special interest since we show that they remain bounded even when these invariants admit the gradient catastrophe. We describe in detail a procedure for constructing such classes of solutions. Finally, we present several examples of an application of our approach which includes bumps, kinks and multi-wave solutions.

Item Type: Article
Uncontrolled Keywords: fluid dynamics, mathematical physics
Subjects: G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
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Depositing User: Dr Benoit Huard
Date Deposited: 26 Mar 2013 14:02
Last Modified: 17 Dec 2023 14:03
URI: https://nrl.northumbria.ac.uk/id/eprint/11571

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