Analytical Studies On The Solitons And Chaos For The Nonlinear Schrodinger Equations

The nonlinear Schrodinger (NLS) equations, which describe the propaga-tion of the nonlinear waves in the nonlinear fibers, photonic crystals, Bose-Einstein condensates and nonlinear optical devices, have been studied. As the nonlinear fiber and optical device develop, the classical NLS equations need to be modified to describe the nonlinear waves dynamics in the different cir-cumstances. For example, when the effects of the Gaussian white noise on the dispersion and nonlinearity are discussed, NLS equations with the stochastic dispersion and nonlinearity need to be studied.Based on these NLS equations, dynamics of the optical soliton pulses are studied with the numerical and analytical methods.For the all-optical switch-ing, ultrashort optical pulse generation and optical pulse amplification, studies on the optical soliton pulse are beneficial. With analytical and numerical meth-ods, dynamics of the optical soliton pulse is discussed to study the physical mechanism. The work of this dissertation includes the following aspects:(1)Study on all-optical soliton switching based on the asymmetric fiber couplers. For the asymmetric coupled NLS equations, self-phase modulation and cross-phase modulation are asymmetric because of the asymmetric effect-s. With analytical and numerical methods, the energy switching of the optical soliton pulses are studied, and the asymmetric fiber couplers can serve as the all-optical switching device. Effects of the varying dispersion and nonlinearity on the dynamics of the optical soliton pulse are discussed.(2)Study on the dynamics of the optical soliton pulse driven by the Gaus-sian white noise in the single-mode fiber. In reality, such models in the nonlin- ear media involve certain uncertainties, so that dispersion and nonlinear param-eters of the NLS equations involve the Gaussian white noises. With the white noise functional approach and Hirota bilinear method, the stochastic soliton so-lutions are obtained. Effects of the Gaussian white noise on the dynamics of the optical soliton pulse are discussed.(3)Study on the optical pulse amplification based on the dispersion-decreasing fiber and fiber coupler. For the dispersion-decreasing NLS equation and NLS coupled equations, mechanism of the optical soliton pulse amplifica-tion are discussed and effects of the fiber parameters on the amplification and periodicity are studied.(4)Study on the chaos of the NLS equation. With the phase space analysis, the chaos based on the nonlinear fiber and fiber device is studied. The optical chaos has the potential application for the chaotic encryption on the all optical communication networks.