Exact Solutions For Two Classes Of Nonlinear Evolution Equations

In this paper,by using trial equation method and polynomial complete discriminant system method,the construction of exact solutions of two kinds of nonlinear models in mathematical physics is studied.Firstly,a kind of light wave model,Schr(?)dinger equation with quadratic cubic nonlinear term,is studied.Through the quartic polynomial discriminant system and trial equation method,the exact envelope mode of the equation is constructed to describe the optical solitons in quadratic cubic nonlinear media.All the exact solutions of the equation are obtained,and the physical realization of the optical wave propagation mode under different parameters is given.These exact solutions show various properties of light wave amplitude modes,including singularity,periodicity and Bi periodicity.Secondly,a kind of water wave model is studied,that is,the exact solution of a kind of coupled KdV equations is constructed.Through the complete discrimination system method and trial equation method of quintic polynomial,all thirteen kinds of exact single wave solutions are obtained,and the dynamic behavior of single wave is completely described.