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

Limei Yan (School of Mathematical Sciences, Dezhou University, Dezhou, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 5 January 2015

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.

Keywords

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

Publisher

:

Emerald Group Publishing Limited

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