Combination Solution Of The Three-component Coupled Nonlinear Schr?dinger Equation

In physics,the coupled nonlinear Schr?dinger equation can be used to describe two or more wave packets propagation in weakly nonlinear media,which is widely used in in many fields.In this paper,we mainly study the characteristics of analytical solution in three-component Coupled nonlinear Schr?dinger equation.The contents of paper are as following :Firstly,we introduce the relevant features and applications of soliton and wave.Secondly,two methods for solving nonlinear Schr?dinger equation is discussed in detail.At last,we mainly study the characteristics of exact soliton in three-component Coupled nonlinear Schr?dinger equation.Using the AKNS procedure,we can get the Lax pairs.In terms of the modified Darboux transformation,we have obtained the exact solution in the three-coupled nonlinear Schr?dinger equation.The explicit andimmediate formalism of these solutions are presented under the continuous wave background.According to the exact solution,we can find that it is a soliton solution when the solutions only are the linear combination of the exponential function which depends on the coordinates.In contrast,the exact solution indicates the rogue wave solution which is combined by the rational polynomial dependence on coordinates.Finally,we give a detailed discussion and analysis for the soliton solution and rogue waves solution.The solutions could be of interest in a variety of complex systems,from optics and fluid dynamics to Bose-Einstein condensates and finance.