Exact Solutions Of Nonlinear Schr(?)dinger-type Equation And Green-Naghdi Equations

In this paper,one effective method for solving the exact solutions of nonlinear evolution equations,namely trial equation method,is used to give the exact traveling wave patterns of two kinds of nonlinear evolution equations.The classifications of solutions are given,and the dynamical behaviors of these two models are shown.Firstly,by using trial equation method,the stationary envelop solutions of the nonlinear Schr(?)dinger-type equation are obtained,including solitary wave solutions,double periodic patterns,soliton solutions and so on.Secondly,by using the same methods,the classification of the exact solutions of the Green-Naghdi equations is given,including solitary waves pattern,blow-up patterns,periodic wave patterns and periodic blow-up double periodic wave patterns.Finally,under the specific parameters,the structures of these solutions for each model can be expressed intuitively through graphs.