论文信息 - Symbolic computation of exact solutions for a nonlinear evolution equation

Symbolic computation of exact solutions for a nonlinear evolution equation

In this paper, by means of the Jacobi elliptic function method, exact double periodic wave solutions and solitary wave solutions of a nonlinear evolution equation are presented. It can be shown that not only the obtained solitary wave solutions have the property of loop-shaped, cusp-shaped and hump-shaped for different values of parameters, but also different types of double periodic wave solutions are possible, namely periodic loop-shaped wave solutions, periodic hump-shaped wave solutions or periodic cusp-shaped wave solutions. Furthermore, periodic loop-shaped wave solutions will be degenerated to loop-shaped solitary wave solutions for the same values of parameters. So do cusp-shaped solutions and hump-shaped solutions. All these solutions are new and first reported here.

[1] Y. Ishimori. On the Modified Korteweg-de Vries Soliton and the Loop Soliton , 1981 .

[2] K. Konno,et al. Some Remarkable Properties of Two Loop Soliton Solutions , 1983 .

[3] E. J. Parkes,et al. The N-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation) , 2003 .

[4] Li Zhi-Bin,et al. An Automated Jacobi Elliptic Function Method for Finding Periodic Wave Solutions to Nonlinear Evolution Equations , 2002 .

[5] Kimiaki Konno,et al. A Loop Soliton Propagating along a Stretched Rope , 1981 .

[6] E. J. Parkes,et al. A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation , 2003 .

[7] Zhao Qiang,et al. A simple fast method in finding particular solutions of some nonlinear PDE , 2001 .

[8] E. Fan,et al. Extended tanh-function method and its applications to nonlinear equations , 2000 .

[9] E. J. Parkes,et al. The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method , 2002 .

[10] E. Parkes,et al. The N-soliton solution of a generalised Vakhnenko equation , 2001, Glasgow Mathematical Journal.

[11] R. Hirota,et al. N-Soliton Solutions of Model Equations for Shallow Water Waves , 1976 .

[12] Wen-tsün Wu. Mechanical Theorem Proving in Geometries: Basic Principles , 1994 .

[13] M. Ablowitz,et al. The Inverse scattering transform fourier analysis for nonlinear problems , 1974 .