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The Extended Tanh Method for Compactons and Solitons Solutions for the CH(<i>n</i>,2<i>n</i> – 1,2<i>n</i>,–<i>n</i>) Equations
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
- 1 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
- 2 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
- 3 School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, China
Journal of Information Security·Volume 03 (2012)·Pages 185–188·Published 25 July 2012·DOI10.4236/jis.2012.33022
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Abstract
In this paper, by using the sine-cosine method, the extended tanh-method, and the rational hyperbolic functions method, we study a class of nonlinear equations which derived from a fourth order analogue of generalized Camassa-Holm equation. It is shown that this class gives compactons, solitary wave solutions, solitons, and periodic wave solutions. The change of the physical structure of the solutions is caused by variation of the exponents and the coefficients of the derivatives.
KeywordsThe CH(<i>n</i>2<i>n</i>– 12<i>n</i>–<i>n</i>) EquationCompactonsSine-Cosine Method and the Extended Tanh MethodRational Hyperbolic Functions Method
- S. Tang, Y. Xiao and Z. Wang, “Travelling Wave Solutions for a Class of Nonlinear Fourth Order Variant of a Generalized Camassa-Holm Equation,” Applied Mathematics and Computation, Vol. 210, 2009, pp. 39-47. doi:10.1016/j.amc.2008.10.041
- W. Malfliet, “Solitary Wave Solutions of Nonlinear Wave Equations,” American Journal of Physics, Vol. 60, No. 7, 1992, pp. 650-654. doi:10.1119/1.17120
- W. Malfliet and W. Hereman, “The Tanh Method: II. Perturbation Technique for Conservative Systems,” Physica Scripta, Vol. 54, 1996, pp. 569-575.
- A. M. Wazwaz, “A Class of Nonlinear Fourth Order Variant of a Generalized Camassa-Holm Equation with Compact and Noncompact Solutions,” Applied Mathematics and Computation, Vol. 165, 2005, pp. 485-501. doi:10.1016/j.amc.2004.04.029
- Z. Y. Yan, “New Explicit Travelling Wave Solutions for Two New Integrable Coupled Nonlinear Evolution Equations,” Physics Letters A, Vol. 292, 2001, pp. 100-106. doi:10.1016/S0375-9601(01)00772-1