标题： 交叉线性和非线性光子晶格中的物质波二维孤子 显示英文标题

标题： Matter-wave 2D solitons in crossed linear and nonlinear optical lattices

摘要： 在具有沿$x-$方向的线性光晶格（OL）和沿$y-$方向的非线性光晶格（NOL）的交叉光晶格中，证明了多维物质波孤子的存在，其中 NOL 可以通过使用光学诱导的 Feshbach 共振对散射长度进行周期性空间调制来产生。特别是，我们表明这种交叉的线性和非线性 OL 可以使二维（2D）孤子在吸引和排斥相互作用下稳定，防止其衰减或坍塌。孤子稳定性的解通过多高斯变分方法（VA）进行分析研究，应用 Vakhitov-Kolokolov（VK）稳定性必要准则；并通过松弛方法和 Gross-Pitaevskii 方程（GPE）的直接数值时间积分进行数值研究。观察到两种处理方法的结果有很好的一致性。 显示英文摘要

摘要： It is demonstrated the existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with linear OL in the $x-$direction and nonlinear OL (NOL) in the $y-$direction, where the NOL can be generated by a periodic spatial modulation of the scattering length using an optically induced Feshbach resonance. In particular, we show that such crossed linear and nonlinear OL allows to stabilize two-dimensional (2D) solitons against decay or collapse for both attractive and repulsive interactions. The solutions for the soliton stability are investigated analytically, by using a multi-Gaussian variational approach (VA), with the Vakhitov-Kolokolov (VK) necessary criterion for stability; and numerically, by using the relaxation method and direct numerical time integrations of the Gross-Pitaevskii equation (GPE). Very good agreement of the results corresponding to both treatments is observed.