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Kudryashov, Nikolai A.; Sinelshchikov, Dmitry I.

An extended equation for the description of nonlinear waves in a liquid with gas bubbles. (English) Zbl 1454.76097

Wave Motion 50, No. 3, 351-362 (2013).
Summary: Nonlinear waves in a liquid with gas bubbles are studied. Higher order terms with respect to the small parameter are taken into account in the derivation of the equation for nonlinear waves. A nonlinear differential equation is derived for long weakly nonlinear waves taking into consideration liquid viscosity, inter-phase heat transfer and surface tension. Additional conditions for the parameters of the equation are determined for integrability of the mathematical model. The transformation for linearization of the nonlinear equation is presented too. Some exact solutions of the nonlinear equation are found for integrable and non-integrable cases. The nonlinear waves described by the nonlinear equation are numerically investigated.

Cited in 5 Documents

MSC:

76T10 Liquid-gas two-phase flows, bubbly flows
35Q35 PDEs in connection with fluid mechanics

Keywords:

liquid with gas bubbles; gas-liquid mixture; nonlinear waves; heat exchange; Painlevé test; integrability
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References:

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