Study of coupled nonlinear partial differential equations for finding exact analytical solutions

Kamruzzaman Khan; M Ali Akbar; H Koppelaar

doi:10.1098/rsos.140406

Study of coupled nonlinear partial differential equations for finding exact analytical solutions

R Soc Open Sci. 2015 Jul 15;2(7):140406. doi: 10.1098/rsos.140406. eCollection 2015 Jul.

Authors

Kamruzzaman Khan¹, M Ali Akbar², H Koppelaar³

Affiliations

¹ Department of Mathematics , Pabna University of Science and Technology , Pabna 6600, Bangladesh.
² Department of Applied Mathematics , University of Rajshahi , Rajshahi 6205, Bangladesh.
³ Faculty of Electrical Engineering, Mathematics and Computer Science , University of Delft , Delft, The Netherlands.

Abstract

Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G'/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of this method for finding these exact solutions is demonstrated. The method is effective and applicable for many other NPDEs in mathematical physics.

Keywords: Drinfel'd–Sokolov–Wilson equation; Painlevé integrable Burgers equation; enhanced (G′/G)-expansion method; nonlinear partial differential equations; solitary wave.