Study On Solutions Of Three Kinds Of Of Nonlinear Schr(?)dinger Equations

The nonlinear partial differential equation is a mathematical model to describe the nonlinear phenomena in nature.The nonlinear Schr(?)dinger equation is the basic equation to describe the quantum system in micro.Solving the nonlinear Schr(?)dinger equation has important scientific significance and application value.In this paper,three kinds of nonlinear Schr(?)dinger equations are studied.The specific research objects,methods and main research results are as follows:1.The(2+1)-dimensional nonlinear Schr(?)dinger equation with variable coefficients is transformed by fractional complex,and a series of new exact traveling wave solutions are ob-tained by using(G’/~2)-expansion method,including hyperbolic function solutions,rational function solutions and trigonometric function solutions.2.The quintic nonlinear Schr(?)dinger equation with third-order dispersion is transformed by traveling wave,then the ordinary differential equation is transformed into integral form,and a series of new exact solutions with parameters are obtained by using cubic polynomial complete discriminant system.3.The generalized unstable nonlinear Schr(?)dinger equation is transformed by traveling wave,and then the ordinary differential equation is transformed into integral form,and nine new exact solutions are obtained by using the quartic polynomial complete discriminant system.