A Study On Nonlinear Characteristics Of Gaussian Pulse

In nonlinear science,soliton is a kind of pulse traveling wave which can keep the shape,amplitude and velocity invariant in the process of propagation.It is the result of the interaction of dispersion / diffraction and nonlinearity.Mathematically,it is a kind of stable,finite energy nondispersive solution of some nonlinear partial differential equations,which generally has the form of sech or tanh function,that is the pulse form.Therefore,the generalized Gauss pulse can also be regarded as a soliton.Starting from the governing equation,the nonlinear Schr?dinger equation,which is satisfied by the pulse propagation in nonlinear media,the effects of fifth-order nonlinearity,self-frequency shift,nonlinear dispersion and external potential on Gauss pulse transmission are discussed by using the distributed Fourier method and the variational method,some research results have been obtained.1.The nonlinear Schr?dinger equation with the cubic-quintic nonlinearity is investigated.The Gauss soliton solution is obtained by using the heuristic method and the stability of the soliton is analyzed by the distributed Fourier method.The results show that when the cubic-quintic nonlinearity intensity response function is a special exponential form,the Gauss pulse can be propagated in a certain distance and the transmission distance increases with the increase of the propagation constant.2.The influence of self-frequency shift caused by Raman scattering in pulses and Kerr dispersion on the transmission of Gauss pulses are studied.The evolution equations of the parameters of Gauss pulse are obtained by using the variational method.The relationships between them,such as amplitude and pulse width,the constraint relation between chirp and pulse width,the evolution of pulse width with propagation distance are analyzed in detail.When the self-frequency shift and Kerr dispersion satisfy certain conditions,the center frequency of the pulse does not jitter and propagating stably in the form of breather within a certain distance.3.The influence of cubic-quintic nonlinearity and Kerr dispersion on transmission of Gauss pulse are discussed.The results show that the cubic-quintic nonlinearity and Kerr dispersion affect the parameters of Gauss pulse.When investigating the effect of Kerr dispersion on pulse width,it is found that whether or not there is Kerr dispersion,the pulse can propagate stably in the form of breather in a certain distance.However,when the Kerr dispersion increases,the intensity of the pulse increases and the peak of the pulse becomes sharp.4.The propagation of Gauss pulses in nonlinear media under the external constant potential and periodic potential is studied.We find that both the amplitude and the period of the external potential affect the transmission of the pulse.Without the external potential or constant potential,the pulse width become wider and the intensity become smaller in the process of pulse propagation,with the increase of the external potential,this trend will be more significant.When the cosine periodic potential is applied,the width and intensity of pulse change periodically during the transmission process and the maximum intensity increases with the transmission distance.The period of pulse variation is related not only to the period of applied potential,but also to its amplitude.With the increase of the amplitude and period of the external potential,the period of pulse variation decrease.