The Dynamics Of Solitons In Bose-Einstein Condensates

Bose-Einstein condensates (BEC) is the hot topic of physics research in recent years. Based on F-expansion method a.nd Hirota method, we investigate the Gross-Pitaevskii equation, which describes the Bose-Einstein condensates, and we obtain the exact multi-soliton solutions. Then we discuss the dynamics of solitons in Bose-Einstein condensates. Especially we discuss the evolution of solitons near Feshbach resonance. The paper is organized as follows:Part I starts from external trapping potential, The macroscopic behavior of BEC matter is highly sensitive to external conditions, and primarily to the external trapping potential. The external potential has many forms, such as harmonic oscillator potential, optical lattice potential, elliptic function potential, double well potential, and so on. In the part I of this paper, Bose - Einstein soliton solutions of the nonlinear Schrodinger equation with time-dependent linear potential are considered. Based on the F-expansion method, we present a number of Jacobian elliptic function solutions. Particular cases of these solutions, where the elliptic function modulus equals 1 and 0, are various localized solutions and trigonometric functions, respectively. Specially, for V_ext = ZF(T) = Z[mg + H cos(ω₁T)], we discussed the Bose-Einstein condensates trapped in the coupling external field with considering the effect of gravity; for F(T) = constant, it describes the wave (Langmuir or electromagnetic) in a linearly inhomoge-neous plasma with cubic nonlinearly.Part II begins with scattering length. The interatomic interactions greatly affect a wide variety of BEC properties, including static properties, such as the size, shape and stability of the condensate, and dynamic properties, like the collective excitation spectrum and soliton and vortex behavior. Theoretical and experimental studies have demonstrated that variation of the s-wave scattering length a_s for Bose and Fermi gases, including a possibility to change its sign, can be achieved by using the Feshbach reso-...