Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations

Kamruzzaman Khan; M Ali Akbar; S M Rayhanul Islam

doi:10.1186/2193-1801-3-724

Exact solutions for (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony equation and coupled Klein-Gordon equations

Springerplus. 2014 Dec 10:3:724. doi: 10.1186/2193-1801-3-724. eCollection 2014.

Authors

Kamruzzaman Khan¹, M Ali Akbar², S M Rayhanul Islam¹

Affiliations

¹ Department of Mathematics, Pabna University of Science & Technology, Pabna, 6600 Bangladesh.
² Department of Applied Mathematics, University of Rajshahi, Rajshahi, 6205 Bangladesh.

Abstract

Abstract: In this work, recently developed modified simple equation (MSE) method is applied to find exact traveling wave solutions of nonlinear evolution equations (NLEEs). To do so, we consider the (1 + 1)-dimensional nonlinear dispersive modified Benjamin-Bona-Mahony (DMBBM) equation and coupled Klein-Gordon (cKG) equations. Two classes of explicit exact solutions-hyperbolic and trigonometric solutions of the associated equations are characterized with some free parameters. Then these exact solutions correspond to solitary waves for particular values of the parameters.

Pacs numbers: 02.30.Jr; 02.70.Wz; 05.45.Yv; 94.05.Fg.

Keywords: DMBBM equation; Exact solutions; MSE method; NLEEs; Solitary wave; cKG equation.