Solitons and periodic solutions of coupled nonlinear evolution equations by using the sine–cosine method

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:

• Solitons
• Sine–cosine method
• Konopelchenko–Dubrovsky equations
• Klein–Gordon equations
• Nizhnik–Novikov–Veselov equations

Acknowledgements

The authors thank the referees for their fruitful comments.