Analysis of a nonlinear surface wind waves model via Lie group method

Abstract

This article focuses on two aspects. Firstly, symmetry analysis is performed for a nonlinear equation which can model surface wind wave patterns in nature. As a byproduct, the similarity reductions and exact solutions of the equation are constructed based on the optimal systems. Secondly, the explicit solutions are considered by the power series method. Moreover, the convergence of the power series solutions are shown.

Keywords

• Nonlinear surface wind waves
• symmetry analysis
• similarity reduction
• power series method