Travelling wave solutions to the proximate equations for LWSW

Abstract

By feat of Maple 17 and a subsidiary ordinary differential equation, a new extension algebraic method is chosen to construct the travelling wave solutions to the proximate equation set involving an arbitrary parameter for long waves over shallow-water. Multiple triangle periodic solutions and new Jacobi elliptic function solutions are obtained. This procedure is applicable to other nonlinear partial differential equations as well.

Keywords

• auxiliary equation
• algebraic method
• travelling wave solutions