The Propagation Characteristics Of The Higher-order Nonlinear Schr?dinger Equation

Optical fiber communication has been widely used in many areas,and optical solitons which play an important role of transmission have aroused great attention in optical fiber communication.By solving the nonlinear Schr?dinger equation which can describe the propagation of ultrashort optical pulses in optical fibers to analyze the propagation properties of optical solitons.In this paper,we investigate the high-order nonlinear Schr?dinger equation and obtain it's soliton solutions.The contents of paper are as following :Firstly,we introduce the emergence and development of solitons.Secondly,we introduce several types of solitons and the phenomenon of modulation instability.Finally,in terms of Darboux transformation we have exactly solved the higher-order nonlinear Schr?dinger equation that describes the propagation of ultrashort optical pulses in optical fibers.We have discussed the modulation instability process in detail and found that the higher-order term has no effect on the MI condition.Under the different conditions we give Kuznetsov-Ma soliton solution and Akhmediev breather of higher-order nonlinear Schr?dinger equation.The former describes the propagation of a bright pulse on a continuous wave background in the presence of higher-order effects and the soliton's peak position is shifted owing to the presence of a nonvanishing background,while the latter describes the modulation instability process that can be used in practice to produce a train of ultrashort optical soliton pulses.