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

Reza Dastranj, a,* Mehdi Nadjafikhahb, and Megerdich Toomaniana

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

Authors :

Reza Dastranj, ^a,* Mehdi Nadjafikhah^b, and Megerdich Toomanian^a

Author Address :

^aDepartment of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.
^bSchool of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran.

*Corresponding author.

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 threedimensional 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.

DOI :

Article Info :

Received : November 18, 2014; Accepted : June 15, 2015.