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.
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