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Chinese Physics Letters

Small Amplitude Solitons in Bose-Einstein Condensates with External Perturbation

王凤姣, 颜晓红, 王登龙

Published Jan 1, 2008• 0 citations
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Abstract

由开发一个小振幅 soliton 近似方法，我们学习经分解在雪茄烟形状的冷凝物与的弱非线性的刺激排斥内部在外部不安潜力的考虑下面的原子相互作用。没有变细和变化，事波浪 solitons 可以由适当地调整力量在形状在长距离上存在并且旅行，这被显示出内部补偿外部不安潜力的效果的原子相互作用。

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由开发一个小振幅 soliton 近似方法，我们学习经分解在雪茄烟形状的冷凝物与的弱非线性的刺激排斥内部在外部不安潜力的考虑下面的原子相互作用。没有变细和变化，事波浪 solitons 可以由适当地调整力量在形状在长距离上存在并且旅行，这被显示出内部补偿外部不安潜力的效果的原子相互作用。
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We develop a perturbation theory for bright solitons of the F=1F=1F=1 integrable spinor Bose-Einstein condensates (BEC) model. The formalism is based on using the Riemann-Hilbert problem and provides the means to analytically calculate evolution of the soliton parameters. Both rank-one and rank-two soliton solutions of the model are obtained. We prove equivalence of the rank-one soliton and the ferromagnetic rank-two soliton. Taking into account a splitting of a perturbed polar rank-two soliton into two ferromagnetic solitons, it is sufficient to elaborate a perturbation theory for the rank-one solitons only. Treating a small deviation from the integrability condition as a perturbation, we describe the spinor BEC soliton dynamics in the adiabatic approximation. It is shown that the soliton is quite robust against such a perturbation and preserves its velocity, amplitude, and population of different spin components, only the soliton frequency acquires a small shift. Results of numerical simulations agree well with the analytical predictions, demonstrating only slight soliton profile deformation.
The dynamics of the weak nonlinear matter solitary waves in two-component Bose–Einstein condensates (BEC) with cigar-shaped external potential are investigated analytically by a perturbation method. In the small amplitude limit, the two-components can be decoupled and the dynamics of solitary waves are governed by a variable-coefficient Korteweg–de Vries (KdV) equation. The reduction to the KdV equation may be useful to understand the dynamics of nonlinear matter waves in two-component BEC. The analytical expressions for the evolution of soliton, emitted radiation profiles and soliton oscillation frequency are also obtained.