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All traveling wave exact solutions of three kinds of nonlinear evolution equations
Meng F.1; Zhang L.3; Wu Y.2; Yuan W.1
2015-11-30
Source PublicationMathematical Methods in the Applied Sciences
ISSN10991476 01704214
Volume38Issue:17Pages:3678-3688
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(z) and simply periodic solutions w(z),w(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.

KeywordElliptic Function Exact Solution Meromorphic Function The Generalized Boussinesq Equation The Klein-gordon Equation
DOI10.1002/mma.3308
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS Subject000368250600007
WOS IDWOS:000368250600007
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Cited Times [WOS]:1   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF COMPUTER AND INFORMATION SCIENCE
Affiliation1.Guangzhou University
2.Curtin University
3.Universidade de Macau
Recommended Citation
GB/T 7714
Meng F.,Zhang L.,Wu Y.,et al. All traveling wave exact solutions of three kinds of nonlinear evolution equations[J]. Mathematical Methods in the Applied Sciences,2015,38(17):3678-3688.
APA Meng F.,Zhang L.,Wu Y.,&Yuan W..(2015).All traveling wave exact solutions of three kinds of nonlinear evolution equations.Mathematical Methods in the Applied Sciences,38(17),3678-3688.
MLA Meng F.,et al."All traveling wave exact solutions of three kinds of nonlinear evolution equations".Mathematical Methods in the Applied Sciences 38.17(2015):3678-3688.
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