Study Of Solitary Wave Solutions In Monomode Optical Fiber

Starting from nonlinear Schrodinger equations with the constant and variable coefficients, we derive the solitary wave solutions of these equations with the help of the methods including the extended hyperbolic function method, the F-expansion method, the Darboux transformation based on Ablowitz-Kaup-Newell-Segur(AKNS) technology and the Adomian decomposition method, and investigate the properties of propagation of fundamental solitary waves and two-solitary waves in monomode optical fiber. What we discussed in this paper may improve the analytic foundation for realizing the transmission of fast-speed and high-capacity optical information systems. Moreover, using the Jacobian elliptic function expansion method, the integrable differential-difference nonlinear Schrodinger equation(AL model) is discussed. The paper is organized as follows:In chapter 1, the research evolution of optical soliton is introduced. Chapter 2 is devoted to presenting some fundamental concepts related to optical soliton, including optical fiber structure and transmission mode, the difference between temporal and spatial solitons, envelop soliton, bright and dark solitons, dispersion effect, nonlinear effect, self-steepening, self-frequency shift, and Gordon-Haus effect, etc. In chapter 3, we briefly introduce some recently developed approaches, such as the extended hyperbolic function method, the F-expansion method, the extended Jacobian elliptic function expansion method, the Darboux transformation based on AKNS technology and the Adomian decomposition method.In chapter 4, we firstly consider the standard nonlinear Schrodinger equation iu_z ± 1/2utt + |u|~2u = 0, and discuss the evolutional behaviors of fundamental soliton and two-soliton solutions. These results indicate that bright and dark fundamental solitons can propagate without distortion. By selecting suitable initial separation between two solitons, they can separately propagate without interaction. The error between approximate solutions and analytical solutions of bright and dark solitons is small, so these approximate solutions approach analytical solutions very well. It demonstrates...