The Extended Tanh Method for Compactons and Solitons Solutions for the CH(*n*,2*n* – 1,2*n*,–*n*) Equations

Affiliation(s)

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.

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.

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.

KEYWORDS

The CH(*n*,
2*n* – 1,
2*n*,
–*n*) Equation; Compactons; Sine-Cosine Method and the Extended Tanh Method; Rational Hyperbolic Functions Method

The CH(

Cite this paper

X. Lin, S. Tang and W. Huang, "The Extended Tanh Method for Compactons and Solitons Solutions for the CH(*n*,2*n* – 1,2*n*,–*n*) Equations," *Journal of Information Security*, Vol. 3 No. 3, 2012, pp. 185-188. doi: 10.4236/jis.2012.33022.

X. Lin, S. Tang and W. Huang, "The Extended Tanh Method for Compactons and Solitons Solutions for the CH(

References

[1] 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

[2] 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

[3] W. Malfliet and W. Hereman, “The Tanh Method: II. Perturbation Technique for Conservative Systems,” Physica Scripta, Vol. 54, 1996, pp. 569-575.

[4] 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

[5] 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

[1] 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

[2] 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

[3] W. Malfliet and W. Hereman, “The Tanh Method: II. Perturbation Technique for Conservative Systems,” Physica Scripta, Vol. 54, 1996, pp. 569-575.

[4] 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

[5] 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