标题： 二维离散孤子在偶极玻色-爱因斯坦凝聚体中 显示英文标题

标题： Two-dimensional discrete solitons in dipolar Bose-Einstein condensates

摘要： 我们分析了在盘状偶极玻色-爱因斯坦凝聚体中亮的非错位孤子的形成和动力学，该凝聚体具有原子之间接触（碰撞）相互作用和长程偶极-偶极（DD）相互作用的相互作用。 假设凝聚体被限制在一个强光学晶格势场中，位于盘的平面内，因此可以近似为一个二维（2D）离散模型，该模型包括位点上的非线性和晶格位点之间的立方长程（DD）相互作用。 我们考虑两种这样的模型，它们的位点非线性形式不同，由通常的立方项表示，或者由从底层三维Gross-Pitaevskii方程导出的更准确的非多项式项表示。 这两种模型都得到了类似的结果。 分析集中在DD相互作用对晶格中基本局域模式（2D离散孤子）的影响上。 排斥各向同性DD非线性扩展了基本孤子的存在和稳定区域。 由于各向同性排斥DD相互作用和吸引接触非线性的相互作用，发现了新的基于有限背景之上的位点、位间和混合孤子族。 这些解本身是不稳定的，但会演化成在振荡背景上存在的稳健呼吸子。 在存在排斥接触相互作用的情况下，如果DD相互作用（吸引各向同性或各向异性）足够强，基本局域模式存在。 它们在接近反连续极限的狭窄区域内是稳定的，而不稳定的孤子则会演化成呼吸子。 在后一种情况下，背景的存在无关紧要。 显示英文摘要

摘要： We analyze the formation and dynamics of bright unstaggered solitons in the disk-shaped dipolar Bose-Einstein condensate, which features the interplay of contact (collisional) and long-range dipole-dipole (DD) interactions between atoms. The condensate is assumed to be trapped in a strong optical-lattice potential in the disk's plane, hence it may be approximated by a two-dimensional (2D) discrete model, which includes the on-site nonlinearity and cubic long-range (DD) interactions between sites of the lattice. We consider two such models, that differ by the form of the on-site nonlinearity, represented by the usual cubic term, or more accurate nonpolynomial one, derived from the underlying 3D Gross-Pitaevskii equation. Similar results are obtained for both models. The analysis is focused on effects of the DD interaction on fundamental localized modes in the lattice (2D discrete solitons). The repulsive isotropic DD nonlinearity extends the existence and stability regions of the fundamental solitons. New families of on-site, inter-site and hybrid solitons, built on top of a finite background, are found as a result of the interplay of the isotropic repulsive DD interaction and attractive contact nonlinearity. By themselves, these solutions are unstable, but they evolve into robust breathers which exist on an oscillating background. In the presence of the repulsive contact interactions, fundamental localized modes exist if the DD interaction (attractive isotropic or anisotropic) is strong enough. They are stable in narrow regions close to the anticontinuum limit, while unstable solitons evolve into breathers. In the latter case, the presence of the background is immaterial.