All traveling wave exact solutions of three kinds of nonlinear evolution equations. (21st October 2014)

• Record Type: Journal Article
• Authors: Meng, Fanning; Zhang, Liming; Wu, Yonghong; Yuan, Wenjun
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 17(2015:Nov. 30)
• Page Start: 3678
• Page End: 3688
• Publication Date: 2014-10-21
• Subjects: exact solution -- meromorphic function -- elliptic function -- the Klein–Gordon equation -- the generalized Boussinesq equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3308
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this article, we employ the complex method to obtain all meromorphic exact solutions of complex Klein–Gordon (KG) equation, modified Korteweg‐de Vries (mKdV) equation, and the generalized Boussinesq (gB) equation at first, then find all exact solutions of the Equations KG, mKdV, and gB. The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic solutions are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions w 2 r, 2 ( z ) and simply periodic solutions w 1 s, 2 ( z ), w 2 s, 1 ( z ) in these equations such that they are not only new but also not degenerated successively by the elliptic function solutions. We have also given some computer simulations to illustrate our main results. Copyright © 2014 John Wiley & Sons, Ltd.