Studies On New Types Of Optical Solitary Waves And Propagation Control Of Optical Pulses In Optical Fiber Communication Systems

Starting from the analytical point of view, we investigate picosecond, sub-picosecond and femtosecond optical pulses' transmission characteristics in an optical fiber or an optical system, including bandwidth-limited gain and higher-order effects with the aid of different methods in solving higher-order derivative differential equation, such as homogenous balance method, anstaz method and Darboux transformation method, also with the aid of different types of perturbation methods, such as momentum method, variation method and numerical method such as symmetrical split-step Fourier transformation method and Lung-Kutta method. Some types of exact steady-state solitary wave solutions are obtained. Then, we further consider the stabilities and interactions of the optical pulses. Our results might provide a more comprehensive theoretical basis to the coming high and ultrahigh capacity of optical information transmitting in both experimental and applied studies. Our research works mainly consist of two parts. Firstly, we start our theoretical investigation from the nonlinear and higher-order nonlinear Schrodinger equations which describe optical pulses propagating in an optical fiber system as well as couple nonlinear and higher-order nonlinear Schroedinger equations which describe optical pulses propagating in a wavelength division multiplexing (WDM) system. Through analytical methods, we find new combined solitary wave solutions of the equations and then we studythe equations and then we study the solutions' stability by numerical methods. Secondly, we theoretically investigate the steady state transmission of optical pulses in inhomogeneous optical fiber media, and also we obtain exact stable solutions. Based on the analytical results, we further consider the pulses interactions and the stabilities in the inhomogeneous optical fiber system. What we discussed in this paper may be helpful to achieve the undistorted transmission and high capacity communication of optical pulses in optical fiber systems. The detailed creative investigation results of this paper are as follows:1) By making use of traveling wave transformation method and homogeneous balance method, we firstly obtain two types of combined solitary wave solutions of higher-order nonlinear Schroed-inger equation. One of which is M-type and can be thought as a dark soliton with finite-width background. And the other one is wavy type. Then by employing the symmetrical split-step Fourier method, we find that these two types of combined solitary wave solutions are very stable during propagation in the optical fiber under the example parameter conditions. Furthermore, we find another steady state combined solitary wave solution of coupled higher-order nonlinear Schroedinger equation which describes the WDM optical communication system. Our results may have potential applications in the coming ultrahigh optical communications.2) By employing the evolution relations of gain dispersion and nonlinear dispersion, we firstly deduce detailedly the higher-order Ginzburg- Landau equation including fourth-order dispersion and other higher-order effects. And then we obtain an exact chirped solitary wave solution of the equation by anstaz method. Through momentum method and linear stability theory, we analyze the solution's stability and obtain the relative parameter space. This result has its meaning not only on optical pulse transmission and optical laser designing, but also on some other physical area such as theapplication of surface waves in fluids, plasma physics, and Bose-Einstein condense (BEC).3) We solve the nonlinear and higher-order nonlinear Schroedigner equation with variable coefficients which govern the optical pulses propagating in inhomogeneous optical fiber media. This provides theoretical basis to the studies of the transmission characteristics of optical bright solitary waves in inhomogeneous optical fiber media and optical soliton control system. Then we firstly obtain the Lax pair of coupled nonlinear and higher-order nonlinear Schroedinger equation with variable coefficients. Based on the Lax pair, we obtain the exact iV-soliton solution of the system. This provide another theoretical basis to the studies of the propagation stabilities and interactions of optical bright solitary waves in inhomogeneous optical fiber systems.