Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations

S M Rayhanul Islam; Kamruzzaman Khan; M Ali Akbar

doi:10.1186/s40064-015-0893-y

Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations

Springerplus. 2015 Mar 12:4:124. doi: 10.1186/s40064-015-0893-y. eCollection 2015.

Authors

S M Rayhanul Islam¹, Kamruzzaman Khan¹, M Ali Akbar²

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

In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.

Keywords: Exact solutions; NLEEs; The KdV equation; The TRLW equation; The exp(−Φ(ξ))-expansion method.