New travelling wave solutions for coupled fractional variant Boussinesq equation and approximate long water wave equation

Abstract

Purpose

The purpose of this paper is to apply the fractional sub-equation method to research on coupled fractional variant Boussinesq equation and fractional approximate long water wave equation.

Design/methodology/approach

The algorithm is implemented with the aid of fractional Ricatti equation and the symbol computational system Mathematica.

Findings

New travelling wave solutions, which include generalized hyperbolic function solutions, generalized trigonometric function solutions and rational solutions, for these two equations are obtained.

Originality/value

The algorithm is demonstrated to be direct and precise, and can be used for many other nonlinear fractional partial differential equations. The fractional derivatives described in this paper are in the Jumarie's modified Riemann-Liouville sense.

Citation

Yan, L. (2015), "New travelling wave solutions for coupled fractional variant Boussinesq equation and approximate long water wave equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 1, pp. 33-40. https://doi.org/10.1108/HFF-04-2013-0126