Solitons and periodic solutions of coupled nonlinear evolution equations by using the sine–cosine method
- 1 December 2006
- journal article
- research article
- Published by Informa UK Limited in International Journal of Computer Mathematics
- Vol. 83 (12), 915-924
- https://doi.org/10.1080/00207160601138756
Abstract
In this paper, we establish exact solutions for coupled nonlinear evolution equations. The sine–cosine method is used to construct exact periodic and soliton solutions of coupled nonlinear evolution equations. Many new families of exact travelling wave solutions of the (2+1)-dimensional Konopelchenko–Dubrovsky equations and the coupled nonlinear Klein–Gordon and Nizhnik–Novikov–Veselov equations are successfully obtained. The obtained solutions include compactons, solitons, solitary patterns and periodic solutions. These solutions may be important and of significance for the explanation of some practical physical problems.Keywords
This publication has 34 references indexed in Scilit:
- Exact solutions for the ZK-MEW equation by using the tanh and sine–cosine methodsInternational Journal of Computer Mathematics, 2005
- The tanh method and the sine–cosine method for solving the KP-MEW equationInternational Journal of Computer Mathematics, 2005
- Backlund transformations for the Nizhnik–Novikov–Veselov equationJournal of Physics A: General Physics, 2004
- On the coherent structures of the Nizhnik–Novikov–Veselov equationPhysics Letters A, 2000
- Two new applications of the homogeneous balance methodPhysics Letters A, 2000
- Lie Symmetries, Kac-Moody-Virasoro Algebras and Integrability of Certain (2+1)-Dimensional Nonlinear Evolution EquationsJournal of Non-linear Mathematical Physics, 1998
- The tanh method: II. Perturbation technique for conservative systemsPhysica Scripta, 1996
- Nonlinear superposition formula of the Novikov-Veselov equationJournal of Physics A: General Physics, 1994
- Compactons: Solitons with finite wavelengthPhysical Review Letters, 1993
- Solitary wave solutions of nonlinear wave equationsAmerican Journal of Physics, 1992