Explicit Rogue Wave Solutions And Dynamic Behavior Of Several Nonlinear Schrodinger Equation

In this paper, we use different methods to construct the rogue wave solutions of nonlinear Schrodinger equation, and use the numerical simulation method to study the propagation law of the rogue wave under the disturbance.The content of this paper is as follows:The first part introduces the research background, significance and research status.The second part introduces the related knowledge of the nonlinear Schrodinger equation and the rogue wave.The third part study the rogue wave solutions of the generalized nonlinear Schrodinger equation.Firstly,we obtain the rogue waves with a controllable center in the generalized nonlinear Schr?dinger equation by using a direct method. The position of these solutions can be controlled by varying different center parameters.Secondly,we study the effects of different parameters on rogue waves and hence find that the nonlinearity parameter is responsible for the width of rogue waves. With the increase of the nonlinearity parameter, the rogue wave becomes wider.Finally, the negative nonlinearity parameter can yield some singular rogue waves.The fourth part the rogue wave solutions of nonlinear Schrodinger equation with variable coefficients are obtained by the method of similarity transformation,and analyze the influence of the parameters on the width and center of rogue wave.Furthemore,we analyze the influence of parameters on the rogue wave height,with the increase or decrease in some parameters, height of wave is also corresponding decrease or increase,so we can through adjusting the parameters to control the appearance or disappearance of the rogue wave.In the fifth part, by using the split-step Fourier method, we study the propagation of solitons and rogue waves in the perturbed Schrodinger equation. Under the disturbance, the soliton can propagate stably, but the rogue wave is easy to collapse and diffuse. Then we find that the parameters’ sensitivity of the rogue wave is very strong, and change of the parameters can cause the great change of the propagation ofthe rogue wave. Therefore, the propagation of rogue waves can be reduced by adjusting the parameters.The sixth part is the summary and prospect.