All traveling wave exact solutions of the variant Boussinesq equations

Wenjun Yuan, Fanning Meng, Yong Huang and Yonghong Wu

Applied Mathematics and Computation, 2015, vol. 268, issue C, 865-872

Abstract: In this article, we employ the complex method to obtain all meromorphic solutions of complex variant Boussinesq equations (1), then find out related traveling wave exact solutions of System (vB). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic solutions wr,1(kx−λt),wr,2(kx−λt),ws,1(kx−λt) and ws,2(kx−λt) of System (vB) are solitary wave solutions, and there exist some rational solutions wr,2(z) and simply periodic solutions ws,2(z) which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. We also give some computer simulations to illustrate our main results.

Keywords: The variant Boussinesq equations; Exact solution; Meromorphic function; Elliptic function (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:268:y:2015:i:c:p:865-872

DOI: 10.1016/j.amc.2015.06.088

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