Construction And Classification Of Exact Solutions For Two Nonlinear Physical Modeling Equations

In this paper,we mainly apply the trial equation method and the complete discrimination system for polynomial method to give the constructions and classifications of exact solutions for two nonlinear physical modeling equations.These exact solutions will be useful in describing the dynamical behaviors of these two models.This article is mainly divided into two parts.The first part is to use the complete discrimination system for polynomial method to give the construction and classification of exact solutions for the nonlinear three-dimensional mKdV-ZK equation.These exact traveling wave solutions include rational function type solutions,Jacobian elliptic function solutions,solitary wave solutions,and trigonometric function periodic solutions.The second part is to study the optical propagation in the birefringent polarization-preserving fiber modeled by the nonlinear Schr?dinger equations system including the effect of four-wave mixing.A general trial equation method for complex coupled system is introduced to give optical solitons and envelope solutions.These rich results show a varied of optical propagation patterns of the model.Under the concrete parameters,we give representations of these optical propagation patterns.