Analyzing the Conservation Law Kudryashov-Sinelshchikov Equation

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 nonlinearpressure waves in a mixture liquid and gas bubbles. The scaling method is the algo- rithmic method which based on calculus, variational calculus, and linear algebra. Inthis method the density of conservation law is obtained by scaling symmetry and the corresponding ux is calculated by homotopy operator. 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) equa- tion , Homotopy operator.