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- Title
All traveling wave exact solutions of three kinds of nonlinear evolution equations.
- Authors
Meng, Fanning; Zhang, Liming; Wu, Yonghong; Yuan, Wenjun
- 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 w2r,2(z) and simply periodic solutions w1s,2(z),w2s,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.
- Subjects
NONLINEAR evolution equations; EVOLUTION equations; NUMERICAL analysis; ASYMPTOTIC expansions; MATHEMATICAL analysis
- Publication
Mathematical Methods in the Applied Sciences, 2015, Vol 38, Issue 17, p3678
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.3308