Conservation Laws of the Kudryashov and Sinelshchikov equation by the Scaling Method

In this paper, we obtain the conservation laws for Kudryashov and Sinelshchikov (K-S) equation by the scaling method.This equation appears in calculation of nonlinear pressure waves in a mixture liquid and gas bubbles. The scalingmethod is the algorithmic method which based on calculus, variational calculus, and linear algebra. In this method thedensity of conservation law is obtained by scaling symmetry and the corresponding flux is calculated by homotopyoperator. We use this method to construct conservation laws of rank ۶, ۷ for the K-S equation.

Keywords:

Scaling symmetry , Conservation law , Kudryashov-Sinelshchikov (K-S) equation , Homotopy operator