All traveling wave exact solutions of the variant Boussinesq equations

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.