Research On Space-time Characteristics Of Optical Soliton Based On Fractional Nonlinear Schrodinger Correlation Equation

Based on the fractional nonlinear Schr(?)dinger correlation equation,the exact solutions of the fractional optical soliton are constructed by the analytic methods based on the generalized MittagLeffler function,such as the generalized fractional Riccati method,the generalized fractional bifunction method and the generalized fractional mapping method.The physical meaning of a series of solutions is illustrated by the dynamic evolution diagrams,and the influence of the Levy index on the propagation characteristics of optical solitons is revealed for us.The Gross-Pitaevskii equation in the Bose-Einstein condensate is similar to the nonlinear Schr(?)dinger equation in nonlinear optics,so this thesis simulates the ring dark soliton in the Bose-Einstein condensate dynamic behavior.On the basis of this research,the existence,stability and dynamic behavior of ring dark solitons and ring anti-dark solitons are studied based on the fractional Schr(?)dinger equation describing the propagation of optical waves in two-dimensional space.The main contents are as follows:1.The soliton solutions of fractional Ginzburg-Landau equation and fractional Gerdjikov-Ivanov equation are constructed.Several fractional exact solutions are constructed,including combined bright solitons,two-hump solitons,periodic waves and singular solitons.The effects of Lévy index on soliton dynamics are revealed through a series of dynamical evolution diagrams of the solutions.2.The discrete soliton solutions of the fractional discrete coupled nonlinear Schr(?)dinger equation are constructed by three generalized fractional analytical methods.Some new analytical discrete solutions are obtained,including discrete fractional bright soliton,dark soliton,combinatorial soliton and periodic soliton solutions.Non-singular solitons composed of coth functions are obtained,and two types of scalar soliton solutions are also obtained.These results have important implications for the further study of complex nonlinear discrete physical phenomena.3.By solving the time-dependent coupled Gross-Pitaevskii equation,it is found that under the modulation of the spin-orbit coupling,the dynamics of the system are more abundant,and the lifetime of the ring dark soliton is greatly extended.After decay,half-quantized vortex pairs are generated,and the vortex pairs separate and recombine many times during the evolution.The evolution of dark soliton and the vortex structure generated after decay also expand new ideas for the in-depth study of nonlinear phenomena in optics.4.The purpose of enhancing the stability of annular dark solitons and annular anti-dark solitons is achieved by adjusting the size of the Levy index.In addition,due to the interaction between the dark soliton and the vortex,the vortex plays a certain role in stabilizing the torus structure of the soliton.Under the influence of the Levy index,ring dark solitons and ring anti-dark solitons can maintain stable transmission over longer distances.This makes it possible to observe ring dark solitons and ring antidark solitons during the experimental study.