Analytic Studies On Exact Solutions Of A Higher-order Nonlinear Schr(?)dinger Equation

Nonlinear evolution equations can describe plasma theory,fluid mechanics,nonlinear optical and other natural phenomena.Based on the higher-order nonlinear Schr(?)dinger equation and the higher-order nonlinear Schr(?)dinger equation with varing coefficents,this paper investigate,analytically and numerically,the transmission of soliton in nonlinear system.In explaining the basic rule of natural phenomenon,the equation with higher-order odd and even terms is more accurate than the normal nonlinear Schr?dinger equations.Firstly,the one-and two-soliton solutions are derived by the Hirota bilinear method.The effects of the higher-order terms and the interactions of two solitons are investigated graphically.Secondly,breather and rogue wave solutions of this equation are constructed via the parameterized Darboux transformation method.Specially,the interactions between two breathers are studied by adjusting the spectral parameters and the collisions between breather and rogue wave are also discussed.Finally,based on the solutions of the higher-order nonlinear Schr(?)dinger equation,we construct the exact solutions of the inhomogeneous higher-order nonlinear Schr(?)dinger equation.