Research On The Exact Solutions Of Two Kinds Of Higher Order Nonlinear Schr(?)dinger Equations

Many phenomena in natural science can be described by partial differential equations.With the rapid development of various fields,partial differential equations are widely used in quantum mechanics,epidemiology,plasma physics,fluid mechanics,ecological economic systems and many other fields.Therefore,it is of great practical significance to construct the solutions of nonlinear partial differential equations.In this paper,polynomial complete discriminant system and trial equation method are applied to solve the exact solutions of two high-order nonlinear Schr(?)dinger equations in optics.The exact solutions obtained can describe some kinetic behaviors of the two physical models.Firstly,the perturbation nonlinear Schr(?)dinger equation is transformed into an ordinary differential equation by traveling wave transformation,and the real part and the imaginary part are separated and set to zero respectively,the complete discriminant system for polynomial method is applied to the perturbed nonlinear Schr(?)dinger equation,and all single envelope traveling wave solutions of this equation are obtained,and the representations of some propagation modes are given under specific parameters.Secondly,the generalized coupled nonlinear Schr(?)dinger equations are transformed into ordinary differential equations by traveling wave transformation,and the real and imaginary parts are separated and set to zero respectively.Soliton solutions and other envelope solutions are obtained by means of trial equation method and polynomial complete discriminant system method.These results show various optical propagation modes of the model.