Influences Of High-order Nonlinear Effects On The Transmission Characteristics Of Three Solutions With Finite Background

In the last few years,the importance of the soliton solutions of the Nonlinear Schr?dinger(NLS)equations on the finite background,particularly in the nonlinear optical area,has long been given attention physically.Since the solutions on the finite background have great amplitudes,which is similar with oceanic rogue wave,they are used in the research of how rogue wave form,which has caused abroad attention.These solutions mainly include Akhmediev breather(AB),Kuznetsov Ma soilton(KMS)and Peregrine soliton(PS).Due to the special properties of breathers,people usually think that PS is the prototype of rogue wave,which have found widespread applications in the supercontinuum generation and obtaining stable high power pulses.Recently,people found the PS in water tank,plasma experiments,and optical fiber systems.AB and KMS are large amplitude waves on the finite background,so they can also be considered the model of rogue wave.In conclusion,on the basis of presented researches,based on the modified self-focusing nonlinear Schr?dinger(NLS)equations with the higher order nonlinear effects(the Raman gain effect,the Self-Steepening,Self-frequency shift effects and third order dispersion),we present the form of exact solutions and the fundamental characteristics of the three solutions on the finite background.Taken no account of the fiber loss,by using of the software of MATLAB and applied the split-step Fourier transform method,the thesis studied detailedly the influence of the higher order nonlinear effects on the transmission properties of three solutions with the finite background,which are the Peregrine rogue wave,Akhmediev breather and Kuznetsov-Ma soliton.According to the comparison of their transmission contour plots and spectrum diagrams,we can obtain the laws of pulses' intensity variation.The simulation results show that the higher order nonlinear effects cause pulses splitting at an increasing rate for PS,AB solution and KMS in temporal domain.The pulses splits faster with the larger high-order nonlinear effect coefficients.The high-order nonlinear effects also make the pulses' peak power at the maxi-suppression point become higher along the transmitting distance,the center of the pulses deviate,and the peaks' interval become shorter with the high-order nonlinear effect increasing.The earlier pulses splitting,the center of the pulse deviates larger.Based on the discussions and researches of this paper,the results will offer some theoretical reference for further comprehension of the dynamics properties of the three solutions on the finite background and their relationship.