Study On Propagation Characteristics Of Soliton In Two Nonlinear Systems

It is undoubtedly a very important problem to find the solutions of the soliton equations which play a kernel role in lots of nonlinear problems. Besides the research on approximate solutions of certain soliton equations using numerical method, finding exact solutions of soliton equations will do great help in understanding the properties of soliton equations. Applying the extended Tanh-function expansion method, exact solutions of two very important nonlinear systems, i.e., nonlinearity management fiber Bragg grating and metamaticals, are gained. The main research results are listed below:Firstly, by using an extended Tanh-Function expansion method, exact solitary solutions are obtained in new nonlinearity management fiber Bragg grating, which is proposed recently. Based on the nonlinear coupled mode equation, which takes nonlinearity management into consideration, the nonlinear coupled mode equation is reduced into the perturbed nonlinear Schr(o|¨)dinger equation through using the multiple scale analysis. Then dark solitary solutions can be constructed by an extended Tanh-Function expansion method. Furthermore, the effects of the physical parameters of nonlinear periodic structure on soliton propagation are discussed, and the required minimum power of soliton is given under various conditions in the fiber Bragg grating structure.Secondly, exact solitary solutions of propagation equation of ultrashort pulse are derived in metamaticals (MMs) by employing the same method. Different from ordinary materials, the MM has a dispersive magnetic permeability, which results in a controllable SS effect and a series higher order nonlinear dispersion items in the ultrashort pulse propagation equation. Based on these exact solutions, the influence of the controllable SS effect and second-order nonlinear dispersion on formation and propagation of dark electromagnetic solitons is discussed. It is found that the negative SS effect in MMs makes the soliton center move to the leading side of soliton, opposite to that in ordinary material in which the SS effect is always positive. Most importantly, due to the role of the second-order nonlinear dispersion, dark solitons can be formed in the absence of linear dispersion, or even in the case of anomalous linear group-velocity dispersion, which gives new visual angle to soliton theory.