Research On Vector Rogue Waves Solutions Of Coupled Nonlinear Schr(?)dinger Equation

The nonlinear Schr(?)dinger equation is widely used in optics,Bose-Einstein condensation,fluid dynamics,plasma physics,molecular biology,and even finance.For many physical systems there are often more than one component,and the coupled nonlinear Schr(?)dinger equation has attracted widespread attention.In this paper,the origin and characteristics of three kinds of rogue waves are introduced firstly: such as ocean rogue waves,optical rogue waves and magnetic rogue waves.Because of its instantaneity and high energy characteristics,we cannot predict the rogue waves in advance.The appearance of the rogue waves will inevitably cause harm to navigation and coastal buildings.This paper lists the harm of the rogue waves,introduces the research model of the rogue waves,and summarizes some research on the rogue waves.In this paper,the coupled nonlinear Schr(?)dinger equation is taken as a model,and the coupled equation is solved by Lax pair and Darboux transform.Then,the exact solutions of the coupled nonlinear Schr(?)dinger equation are discussed from two parts: one eigenfunction and the other two eigenfunctions.In the case of a series of eigenfunctions,the symmetrical rogue waves can be obtained for the coupled nonlinear Schr(?)dinger equation with the double-seed solution,while the asymmetrical rogue waves for single-seed solution.In order to better understand the formation mechanism of the rogue waves,we analyzed the energy characteristics of the rogue wave,and explained the formation process of the rogue wave through the non-uniform exchange between the plane wave background and the rogue wave.The results of the exchange rate show that the energy in the background first accumulates to the central part,resulting in a crest with a groove on the background,and a critical value of the crest may appear.Then,the energy of the rogue waves begins to dissipate into the background,so that the crest gradually decays to the final disappearance.It also proves that the rogue wave is only an oscillation in time location and shows unstable dynamic behavior.Following,we study the rogue waves in the case of two eigenfunctions,we get different kinds of rogue waves by adjusting the parameters in the exact solution of rogue waves,and we analyze different types of asymmetric rogue waves by using the exchange rate.