New solutions for solving Boussinesq equation via potential symmetries method

Mina B. Abd-el-Malek, Nagwa A. Badran, Hossam S. Hassan and Heba H. Abbas

Applied Mathematics and Computation, 2015, vol. 251, issue C, 225-232

Abstract: This work deals with the Boussinesq equation that describes the propagation of the solitary waves with small amplitude on the surface of shallow water. Firstly, the equation is written in a conserved form, a potential function is then assumed reducing it to a system of partial differential equations. The Lie-group method has been applied for determining symmetry reductions of the system of partial differential equations. The solution of the problem by means of Lie-group method reduces the number of independent variables in the given partial differential equation by one leading to nonlinear ordinary differential equations. The resulting non-linear ordinary differential equations are then solved numerically using MATLAP package.

Keywords: Boussinesq equation; Potential method; Similarity solutions; Lie group (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:251:y:2015:i:c:p:225-232

DOI: 10.1016/j.amc.2014.11.055

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