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arXiv 0709.3399nlin.PS
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旋转晶格中的二维离散孤子

Two-dimensional discrete solitons in rotating lattices

J. Cuevas, B. A. Malomed, P. G. Kevrekidis

备注：
To be published in Physical Review E
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摘要：

在旋转坐标系中引入了一个具有自吸引立方非线性项的二维离散非线性薛定谔方程。该模型适用于玻色-爱因斯坦凝聚体搅拌旋转强光学晶格，或光传播的扭曲束的非线性光纤。构造了两种局域态：离轴基孤子（FS），放置在距离旋转枢轴$R$，和轴上（R=0）涡旋孤子（VS），与涡度$% S=1$和2。在旋转频率$Ω$的固定值下，根据晶格耦合常数$C$，$% 0<C<C_{\mathrm{cr}}(R)$，发现FS的稳定区间，其中$C_{\mathrm{cr}}(R)$单调减小。S=1的VS具有稳定性区间$\tilde{C}_{\mathrm{cr}%}^{(S=1)}(Ω)<C<C_{\mathrm{cr}}^{(S=1)}(Ω)$，其存在于低于特定临界值$Ω_{\mathrm{cr}}^{(S=1)}$的$% Ω$。这意味着S=1的VS在旋转的弱耦合极限下是\emph{destabilized}。相反，已知在标准DNLS方程中不稳定的S=2的VS，具有$Ω=0$，通过在区域$0<C<C_{\mathrm{cr}}^{(S=2)}$ %中的旋转是\emph{stabilized}，其中$C_{\mathrm{cr}}^{(S=2)}$作为$Ω$的函数增长。四极和八极轴上孤子也被认为是，其稳定区域的影响很小的$Ω\neq 0$。

英文摘要：

We introduce a two-dimensional (2D) discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two species of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance $R$ from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities $% S=1$ and 2. At a fixed value of rotation frequency $Ω$, a stability interval for the FSs is found in terms of the lattice coupling constant $C$, $% 0<C<C_{\mathrm{cr}}(R)$, with monotonically decreasing $C_{\mathrm{cr}}(R)$. VSs with S=1 have a stability interval, $\tilde{C}_{\mathrm{cr}%}^{(S=1)}(Ω)<C<C_{\mathrm{cr}}^{(S=1)}(Ω)$, which exists for $% Ω$ below a certain critical value, $Ω_{\mathrm{cr}}^{(S=1)}$. This implies that the VSs with S=1 are \emph{destabilized} in the weak-coupling limit by the rotation. On the contrary, VSs with S=2, that are known to be unstable in the standard DNLS equation, with $Ω=0$, are \emph{stabilized} by the rotation in region $0<C<C_{\mathrm{cr}}^{(S=2)}$%, with $C_{\mathrm{cr}}^{(S=2)}$ growing as a function of $Ω$. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by $Ω\neq 0$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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