Nonlinear Dynamics Of One-Dimensional Spin Chain And Spinor Bose-Einstein Condensates In An Optical Lattice

In this thesis the nonlinear dynamics of one-dimensional spin chain and spinor Bose-Einstein condensates in an optical lattice are investigated by means of an inverse scattering transformation and Darboux transformation.Exact N-soliton trains in a spin chain driven by a time-dependent magnetic field are obtained by means of an inverse scattering transformation. The one-soliton solution indicates obviously the spin precession around the magnetic field and periodic shape variation induced by the time-varying field as well. In terms of the general soliton solutions. N-soliton interaction and particularly various two-soliton collisions are analyzed. The inelastic collision by which we mean the soliton shape change before and after collision appears is generally due to the time-varying field. We, moreover, show that complete inelastic collisions can be achieved by adjusting spectrum and field parameters. This may lead to a potential technique of shape control of soliton.Employing a straightforward Darboux transformation we construct exact N-soliton solution for anisotropic spin chain driven by an external magnetic field in plane wave background. As a special case the explicit one- and two-soliton solution dressed by the plane wave corresponding to magnon in quantum theory is obtained analytically and its property is discussed in detail. The dispersion law, the effective soliton mass, as well as the energy of each soliton are investigated.In the presence of a spin-polarized current the motion of the magnetization of conducting ferromagnet can be described by a modified Landau-Lifshitz equation. From the analytical solution effects of spin current on the frequency, wave number, and dispersion law of spin...