Analytical Analysis Of The Basic Characteristics Of Spatiotemporal Soliton Based On F-expansion Technique

The emergence and development of the soliton theory is a very significantevent in the research of nonlinear equations, with the deepening of the soliton theory,many nonlinear equations which have soliton solutions are found in solid statephysics, fluid physics, superconductivity physics, plasma physics, particle physicsand other fields, to find the exact solutions of nonlinear equations has a great helpfor understanding the nature of the equations and the practical significance behindthese equations, so for nonlinear equations and their solution method has arousedkeen interest of many scientists.This paper first analyzes the soliton theory which is very important innonlinear optical, illustrated three different types of soliton, and then derive theirnonlinear Schrodinger equation which they respectively satisfied. Next discussseries of nonlinear equations with stable soliton solution, gives the inversescattering method, perturbation method and the F-expansion method and othercommonly used analytical methods.One of the major goals in the study of nonlinear wave interactions in optics isthe generation of pulses that are localized in all the transverse dimensions of space,as well as in time, and (2+1+1) D spatiotemporal soliton just has this property, so inthis paper we describe more detail about the spatiotemporal solitons, from theoryand experiment two aspects discussion about the characteristics of spatiotemporalsolitons, and also we analysis its mathematical model.Finally, about the model of cubic-quintic(CQ) which spatiotemporal solitoncan stable in, expand the F-expansion method to use in the generalized nonlinearSchrodinger equation in this model, found a stable solution of spatiotemporalsoliton, in this solution we take different forms of the elliptic function can get brightand dark spatiotemporal solution, then discuss the impact of the chirp to these two solutions, results show that the impact of the chirp on bright and darkspatiotemporal soliton is basically the same, without chirp, the spatiotemporalsoliton propagation stable along coordinate z, but when we think about the chirp, nomatter up-chirp or down-chirp, the intensity of soliton oscillation rapidly, but thedifference of energy distribution between these two cases is similar to the situationof spatiotemporal soliton, when the energy in the case of up-chirp reached theminimum, at the same time with the down-chirp reached the maximum. In addition,the chirp parameter also has great impact, within a reasonable range, the greater thechirp is, the more powerful of the soliton oscillation is, but when exceed this range,the soliton will decay rapidly.