Travelling Wave Solutions To Some Nonlinear Evolution Systems

Many nonlinear problems are described the end results of nonlinear partial differentialequations, so finding exact solutions to nonlinear partial differential equations have becomean important problem in nonlinear science. In particular, obtaining exact solutions to anonlinear evolution system are more complex and difficulty than a nonlinear evolutionequation. In this paper, we consider the six nonlinear evolution systems, including thenonlinear model contacted with the Sch o dingerequation, the modified Boussinesq system,the long wave system, the ariable Konopelchenko-Dubrovsky system, the rank-homogeneouscoupled Kdv system and rank-nonhomogeneous high-dimension coupled Burgers system. Onone hand using the method of complete discrimination system for polynomial, we give theclassifications of all the single traveling wave solutions to the first four systems. On the otherhand, using the trial equation method, a lot of single traveling wave solutions to the later twosystems are obtained.