Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method

Md Nur Alam; M Ali Akbar; Harun-Or- Roshid

doi:10.1186/2193-1801-3-43

Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G'/G)-expansion method

Springerplus. 2014 Jan 23:3:43. doi: 10.1186/2193-1801-3-43. eCollection 2014.

Authors

Md Nur Alam¹, M Ali Akbar², Harun-Or- Roshid¹

Affiliations

¹ Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh.
² Department of Applied Mathematics, University of Rajshahi, Rajshahi, Bangladesh.

Abstract

Abstract: Exact solutions of nonlinear evolution equations (NLEEs) play a vital role to reveal the internal mechanism of complex physical phenomena. In this work, the exact traveling wave solutions of the Boussinesq equation is studied by using the new generalized (G'/G)-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. It is shown that the new approach of generalized (G'/G)-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations in mathematical physics and engineering.

Pacs: 05.45.Yv, 02.30.Jr, 02.30.Ik.

Keywords: Homogeneous balance; New approach of generalized (G′/G)-expansion method; Nonlinear evolution equation; The Boussinesq equation; Traveling wave solutions.