Travelling Wave Solutions of Nonlinear Evolution Equation by Using an Auxiliary Elliptic Equation Method

Abstract:

The Camassa-Holm and Degasperis-Procesi equation describing unidirectional nonlinear dispersive waves in shallow water is reconsidered by using an auxiliary elliptic equation method. Detailed analysis of evolution solutions of the equation is presented. Some entirely new periodic-soliton solutions, include Jacobi elliptic function solutions, hyperbolic solutions and trigonal solutions, are obtained. The employed auxiliary elliptic equation method is powerful and can be also applied to solve other nonlinear differential equations. This method adds a new route to explore evolution solutions of nonlinear differential equation.

• Periodical: Applied Mechanics and Materials (Volumes 166-169)
• Pages: 3228-3232
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.166-169.3228
• Online since: May 2012
• Authors: Chun Huan Xiang
• Keywords: Auxiliary Elliptic Equation, Camassa-Holm and Degasperis-Procesi Equation, Hyperbolic Solutions, Nonlinear Evolution Equation, Numerical Simulation, Travelling Wave Solutions, Trigonal Solutions

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