Analytic Study On The Nonlinear Schr(?)dinger Models And Their Applications

There are a large number of complex nonlinear phenomena in nature.The essence of these phenomena is revealed by constructing suitable non-linear models.Nonlinear Schr(?)dinger equation,as a kind of very impor-tant equation in the nonlinear model,can be used to describe the nonlin-ear phenomena in various fields such as nonlinear optics.Bose-Einstein condensation,plasma physics,optical communication.Solitons have been widely used in many fields of natural sciences due to their properties of invariant shape and velocity during transmission.Analytical study of soli-tons based on nonlinear Schr(?)dinger equation is of practical significance both in the development of soliton theory and in the development and improvement of specific applications.Combining with the current development of soliton in different fields.the Hirota bilinear method is used to study the optical soliton interaction in optical fiber systems which is described by the nonlinear Schr(?)dinger equation,and the soliton dynamic behavior in Heisenberg ferromagnet-ic chain is explored.The soliton interaction phenomenon found in the system is analyzed.The specific research cont,ents are as follows:(1)Soliton generation and interaction in dispersion-decreasing fiber-s:For the variable coefficient high-order nonlinear Schr(?)dinger equation,analytic two-and three-soliton solutions are derived by the Hirota bi-linear method.Optical solitons propagation in the dispersion-decreasing fibers is investigated theoretically.The influence of corresponding pa-rameters is discussed based on obtained solutions.By choosing properly parameters,optica.l solitons are amplified and reshaped stably in a long distance.Besides,the number of amplified solitons can be chosen as re-quired.Moreover,a novel phenomenon that three solitons can split into four solitons or merge into two solitons has been proposed.Results may be helpful to realize the amplification,reshaping,fission and annihilation of solitons,and will be valuable to the applications of optical amplifier,all-optical switching and optical self-routing.(2)Soliton pulse compression and spatiotemporal pulse-train solitons generation in optical fiber:One-and two-soliton analytical solutions of a fifth-order nonlinear Schr(?)dinger equation with varia,ble coefficients are derived by means of the Hirota bilinear method.Various scenarios of one-soliton shaping and two-soliton interaction and reshaping are inves-tigated,using the obtained exact solutions and adjusting parameters of the model.It has been found that widths of two colliding solitons can change without changing their amplitudes.Furthermore,two originally bound solitons are separated and are then moving in opposite direction-s.Two colliding solitons can fuse to form a spatiotemporal pulse-train,composed of equally separated identical pulses.Moreover,the width and propagation direction of the spatiotemporal pulse-train can change simul-taneously.Effects of corresponding parameters on the one-soliton shaping and two-soliton interaction are discussed.Results of this paper may be beneficial to the application of optical self-routing,switching and path control.(3)Soliton interaction in the Heisenberg ferromagnetic spin chain:Interactions of bright solitons in the Heisenberg ferromagnetic spin chain,governed by a(2+1)-dimensional nonlinear Schr(?)dinger equation with variable coefficients,are investigated theoretically.Analytical soliton so-lutions are derived by means of the Hirota bilinear method.Different sce-narios of soliton propagation and interactions are illustrated.The influ-ence of relevant parameters and variable coefficients of different function types on the soliton propagation and interactions is discussed.Solitons of different shapes in propagation,whose pulse widths and oscillation peri-ods vary with the phase shift,are presented.The method for controlling the size of the phase shift is proposed.Furthermore,the fission soliton-s and the bound solitons,produced after their collisions,are displayed.Methods for controlling the number and amplitudes of fission solitons,the distance between solitons and the intensity of their interactions are put forward.Results in this paper will contribute to the effective control of solitons in the Heisenberg ferromagnetic spin chain system.