Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity.
Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity.
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DOI：
10.1103/physreve.73.026601
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发表时间：
2006-01
期刊：
影响因子：
--
通讯作者：
H. Sakaguchi;B. Malomed
中科院分区：
文献类型：
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作者：
H. Sakaguchi;B. Malomed
基于二维Gross-Pitaevskii方程，建立了玻色-爱因斯坦凝聚体的动力学模型，其中非线性系数是半径的函数。该模型描述了一种负原子散射长度空间调制的情况，这种情况是通过适当形状的磁场或光场控制的费什巴赫共振实现的。我们重点研究了在圆或环空中非线性系数不为零的构型，包括窄环的情况。二维轴对称孤子有数值形式，也有变分近似形式；对于无限窄的环，孤子以精确形式存在（在后一种情况下，精确孤子也存在于双组分模型中）。通过数值和解析方法确定了孤子的稳定区域。特别地，如果非线性被支撑在环上，则上稳定边界由方位摄动决定；当环空内外半径之比超过临界值时，稳定区消失。由于静态孤子与稳定轴对称呼吸子共存，该模型产生了双稳性，稳定呼吸子的稳定区域比静态孤子扩展到更高的范数值。塌陷阈值随环空内孔半径的增大而增大。涡旋孤子也被发现，但它们是不稳定的。
We introduce a dynamical model of a Bose-Einstein condensate based on the two-dimensional Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative atomic scattering length, via the Feshbach resonance controlled by a properly shaped magnetic of optical field. We focus on the configuration with the nonlinear coefficient different from zero in a circle or annulus, including the case of a narrow ring. Two-dimensional axisymmetric solitons are found in a numerical form, and also by means of a variational approximation; for an infinitely narrow ring, the soliton is found in an exact form (in the latter case, exact solitons are also found in a two-component model). A stability region for the solitons is identified by means of numerical and analytical methods. In particular, if the nonlinearity is supported on the annulus, the upper stability border is determined by azimuthal perturbations; the stability region disappears if the ratio of the inner and outer radii of the annulus exceeds a critical value . The model gives rise to bistability, as the stationary solitons coexist with stable axisymmetric breathers, whose stability region extends to higher values of the norm than that of the static solitons. The collapse threshold strongly increases with the radius of the inner hole of the annulus. Vortex solitons are found too, but they are unstable.