Extended two dimensional equation for the description of nonlinear waves in gas–liquid mixture

Nikolay A. Kudryashov, Dmitry I. Sinelshchikov and Alexandr K. Volkov

Applied Mathematics and Computation, 2015, vol. 268, issue C, 581-589

Abstract: We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the description of density perturbations of mixture in the two-dimensional case. We investigate integrability of this equation using the Painlevé approach. We show that traveling wave reduction of the equation is integrable under some conditions on parameters. Some exact solutions of the equation derived are constructed. We also perform numerical investigation of the nonlinear waves described by the derived equation.

Keywords: Nonlinear equation; Nonlinear wave; Liquid with gas bubbles; Reductive perturbation method; Painlevé test; Exact solutions (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:581-589

DOI: 10.1016/j.amc.2015.06.095

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