Analysis Of Rogue Wave Solutions For Coupled Nonlinear Schr(?)dinger Equations

The rogue wave is a common local wave in a nonlinear physical system.It has the characteristics of high amplitude,rapid rise and fast fall.It is known to have high nonlinearity.The rogue wave solution can be expressed by the analytical solution of the nonlinear partial differential equation,and this solution is expressed as a rational function of time and space coordinates.In this paper,the two-component coupled nonlinear Schr(?)dinger equation with coherent coupling term is taken as the research model,and a series of coupled rogue wave nonlinear solutions of the Schr(?)dinger equation are obtained by using the Darboux transform methods.The main contents of this paper are:Firstly,the discovery and cognition of rogue waves are introduced.The rogue wave phenomenon is first discovered in the ocean.Then,in other fields,the existence of rogue waves,such as optical fiber and finance,is also found.In recent years,many researchers have used the nonlinear Schr(?)dinger equation to describe the rogue wave solution.The rogue wave solution obtained by the nonlinear Schr(?)dinger equation can well describe the evolution characteristics of the rogue wave.Therefore,more and more researchers are starting to study rogue waves.Then the method of solving the coupled nonlinear Schr(?)dinger equation is introduced.In this paper,the improved Darboux transform is used to calculate the exact rogue solution of the two-component coupled nonlinear Schr(?)dinger equation.For the two-component rogue wave solution,when one seed solution exists or two seed solutions exist,by adjusting the size of some parameter values in the rogue wave solution,the asymmetric rogue wave solution of the single seed solution can be obtained.The symmetry and asymmetry rogue wave solution of two-seed solution.In addition,numerical simulation and analysis of these rogue wave solutions have obtained many rogue waves of different structures,such as bright rogue waves,petal-type rogue waves and two peaks and four valleys.By adjusting the positive and negative and the magnitude of the wave vector in the rogue wave solution,it can be seen that the wave vector affects the direction of rotation and the degree of rotation of the rogue wave.In order to understand the generation mechanism of these rogue waves,by analyzing and discussing the non-uniform exchange rate distribution image of the rogue wave,it can be known that the larger the exchange rate value,the more obvious the dispersion degree,and the more obvious the rogue wave characteristics.Thus,a mechanism for generating rogue waves is the accumulation of energy and the movement of the particles toward the center,and more understanding of the exchange of particle numbers and energy between the rogue wave and the background.In order to determine the peak-valley form of the rogue wave in the time and space range,the density distribution image can be analyzed.The function value is greater than zero,indicating that the peak characteristic is obvious,and the function value is less than zero,indicating that the valley characteristic is obvious.These findings are expected to be applied to complex systems such as fluid mechanics,Bose-Einstein condensation,and the transmission of optical signals in optical fibers.