Application of the Kudryasov method with characteristic set algorithm to solve some partial differential equations in fluid mechanics

Abstract

In this paper, we pay attention the analytical method named, the Kudryashov method combined with characteristic set algorithm for finding the exact travelling solutions of two non-linear PDE in fluid mechanics, which named surface wave equation and the generalized Kuramoto-Sivashinsky equation. The solution procedure of the Kudryashov method can be reduced to solve a large system of algebraic equations, which is hard to solve, then we use characteristic set algorithm to solve this problem. The obtained results show that the Kudryashov method combined with characteristic set algorithm is effective.