Traveling Wave Solutions Of Two Types Nonlinear Schr(?)dinger Models And Its Stability Analysis

The nonlinear partial differential equation(NLPDE)is one of the important branch of modern mathematics,which are widely used in nonlinear optics,fluid mechanics,elastic media,plasma objects,signal propagation and other fields.The nonlinear Schr(?)dinger(NLS)equation is one of the most important models,which is often used to describe the complex physical phenomena in real life.However,when we want to explain the phenomenon of principle,it is necessary to solve and analyze the established model.Therefore,it is particularly important to find a suitable and efficient method,which also lays a foundation for the subsequent theoretical explanation.In this paper,the exponential rational function method is improved,the modified exponential rational function method is used to construct many exact traveling wave solutions and solitary wave solutions of the unstable NLS equation,the modified unstable NLS equation,the higher order NLS equation with cubic-quintic dispersion and the generalized NLS equation with second order spatiotemporal nonlinearity,including trigonometric,hyperbolic,rational,exponential functions and lots of other forms,the auxiliary equation method used to obtain the traveling wave solutions of the unstable NLS equation and the modified unstable NLS equation.With the help of Mathematica software,through granting the appropriate parameters,some solutions for different shapes of three-dimensional plots,planar plots and contour plots are shown,the results show different internal structures,such as bright-dark solitons,kink and anti-kink solitons,multi peak solitons,breathers type waves of strange structures,periodic waves and so on,this provides a theoretical basis for explaining some complex physical phenomena.Finally,the stability of the obtained solutions are tested according to the properties of Hamiltonian system,the results prove the effectiveness and superiority of the modified exponential rational function method and provide a feasible and efficient method for solving a class of NLS equation.