Local conservation laws, symmetries, and exact solutions for a Kudryashov‐Sinelshchikov equation

In this paper, we consider a Kudryashov‐Sinelshchikov equation that describes pressure waves in a mixture of a liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer between liquid and gas bubbles. We show that this equation is rich in conservation laws. These...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2018-03, Vol.41 (4), p.1631-1641
Main Authors: Bruzón, M. S., Recio, E., de la Rosa, R., Gandarias, M. L.
Format: Article
Language:English
Subjects:
Bubbles
Conservation laws
Differential equations
Elastic waves
exact solutions
Lie groups
multiplier method
Ordinary differential equations
partial differential equations
symmetries
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Summary:In this paper, we consider a Kudryashov‐Sinelshchikov equation that describes pressure waves in a mixture of a liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer between liquid and gas bubbles. We show that this equation is rich in conservation laws. These conservation laws have been found by using the direct method of the multipliers. We apply the Lie group method to derive the symmetries of this equation. Then, by using the optimal system of 1‐dimensional subalgebras we reduce the equation to ordinary differential equations. Finally, some exact wave solutions are obtained by applying the simplest equation method.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4690