The Study Of Spatial Solitons Supported By Complex Potentials In Competing Cubic-quintic Nonlinearities

The spatial optical soliton is a space domain,when the beam is affected by diffraction effect and nonlinear effect at the same time,the effects of the two effects cancel each other out to reach an equilibrium state and keep it in a stable state.Relying on this characteristic,spatial optical solitons can be applied in many fields,and many applications in all-optical devices and networks,signal processing,etc.have been realized.In order to explore the possibility of spatial optical soliton,it is necessary to conduct further research in theory and discover its various interesting transmission properties.1.Using nonlinear Schr?dinger equation as the basic equation to establish a theoretical model.To obtain the soliton solution,using modified squared-operator iteration method,and the plane wave expansion method is used to calculate the band gap structure of the optical lattice.In addition,linear stability analysis of the soliton solution is performed by Fourier collocation method,and separately simulated soliton propagation by means of split-step Fourier method.It is effective for various properties of solitons are studied to use these methods.2.Using nonlinear Schr?dinger equation containing competing cubic-quintic nonlinearities and non-parity-time（PT）-symmetric complex potentials as the basic equation to establish a theoretical model.The theoretical model is used to study the propagation characteristics of single-peak solitons and out-of-phase double-peak solitons.Below the phase transition point,single-peak and two-peak solitons respectively bifurcate from thelargest and the second largest discrete eigenvalues of the linear spectra.The stability domain of these solitons can also be found.Above the phase transition point,single-peak solitons can transmit stably in a moderate power region.There are also continuous two-peak soliton families when above phase transition,but these two-peak solitons are unstable.3.Using nonlinear fractional Schr?dinger equation containing competing cubic-quintic nonlinearities and parity-time（PT）-symmetric optical lattices as the basic equation to establish a theoretical model.The theoretical model is used to study the propagation characteristics of single-peak solitons,out-of-phase two-peak solitons,and in-phase threepeak solitons.Two-peak solitons and three-peak solitons respectively bifurcate from the semiinfinite gap and the first finite band gap of the optical lattice.The stability domain of these solitons can also be found.And under the influence of focusing effect,defocusing effect and Levi index,both two-peak solitons and three-peak solitons can find corresponding stable intervals.The single-peak solitons cannot exist stably.