Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates
Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates
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DOI：
10.1103/physreva.72.033611
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发表时间：
2005-09-01
影响因子：
2.9
通讯作者：
Liu, WM
中科院分区：
文献类型：
--
作者：
Li, L;Li, ZD;Liu, WM
基于三个非线性耦合的Gross-Pitaevskii方程组，我们在玻色-爱因斯坦凝聚体的旋量(三分量)模型的一般(不可积)模型中发现了极性和铁磁性(FM)型的单分量、二分量和三分量孤子。用直接模拟的方法研究了孤子的稳定性，部分用线性化的小扰动方程进行了解析研究。通过能量比较的方法研究了孤子的全局稳定性。结果识别出FM和极化型孤子的基态和亚稳态孤子态。对于模型的特殊可积形式，我们发展了达布变换(DT)。作为DT的应用，得到了显示由空间周期小扰动引起的连续波态调制不稳定性的完全非线性演化的解析解。此外，借助于直接模拟，我们证明了在可积系统中发现的极型和FM型孤子在结构上是稳定的，即它们在相关的非线性系数随时间随机变化时是鲁棒的。
We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (nonintegrable) model of a spinor (three-component) model of the Bose-Einstein condensate, based on a system of three nonlinearly coupled Gross-Pitaevskii equations. The stability of the solitons is studied by means of direct simulations and, in a part, analytically, using linearized equations for small perturbations. Global stability of the solitons is considered by means of an energy comparison. As a result, ground-state and metastable soliton states of the FM and polar types are identified. For the special integrable version of the model, we develop the Darboux transformation (DT). As an application of the DT, analytical solutions are obtained that display full nonlinear evolution of the modulational instability of a continuous-wave state seeded by a small spatially periodic perturbation. Additionally, by dint of direct simulations, we demonstrate that solitons of both the polar and FM types, found in the integrable system, are structurally stable; i.e., they are robust under random changes of the relevant nonlinear coefficient in time.