Invariant solutions and conservation laws for a three-dimensional K-S equation

Reza Dastranj; Mehdi Nadjafikhah; Megerdich Toomanian

doi:10.26637/mjm303/008

Abstract

In this paper, we study three-dimensional Kudryashov-Sinelshchikov (K-S) equation, which describes long nonlinear pressure waves in a liquid containing gas bubbles. Firstly, We find the symmetry groups of the K-S equation. Secondly, using the symmetry groups, exact solutions which are invariant under a three-dimensional subalgebra of the symmetry Lie algebra are derived. Finally, by adding Bluman-Anco homotopy formula to the direct method local conservation laws of the K-S equation are obtained.

Keywords:

Three-dimensional Kudryashov-Sinelshchikov equation, Lie symmetry analysis, Invariant solution, Conservation laws

Mathematics Subject Classification:

58J70, 76M60, 35L65

Authors Imprint References Funding Related Articles Downloads

Reza Dastranj Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
Mehdi Nadjafikhah School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran.
Megerdich Toomanian Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

Pages: 296-302
Date Published: 01-07-2015
Vol. 3 No. 03 (2015): Malaya Journal of Matematik (MJM)

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