光晶格中多维玻色-爱因斯坦凝聚体的能隙-汤斯孤子和离域跃迁
Gap-Townes solitons and delocalizing transitions of multidimensional Bose-Einstein condensates in optical lattices
摘要：
我们证明了具有吸引相互作用的多维Gross-Pitaeviskii方程以及二维和三维光晶格中间隙汤斯孤立子的存在性。在没有周期势的情况下，该解简化为已知的多维非线性薛定谔方程的汤斯孤子，与这些汤斯孤子共享对小范数（原子数）变化不稳定的特性。我们表明，在存在的光晶格的解决方案分离稳定的本地化解决方案（间隙孤子）从衰减的，特征的离域过渡发生在多维的情况下。讨论了这些高维解与具有高阶非线性项的一维非线性薛定谔方程解之间的联系。
英文摘要：
We show the existence of gap-Townes solitons for the multidimensional Gross-Pitaeviskii equation with attractive interactions and in two- and three-dimensional optical lattices. In absence of the periodic potential the solution reduces to the known Townes solitons of the multi-dimensional nonlinear Schrödinger equation, sharing with these the propriety of being unstable against small norm (number of atoms) variations. We show that in the presence of the optical lattice the solution separates stable localized solutions (gap-solitons) from decaying ones, characterizing the delocalizing transition occurring in the multidimensional case. The link between these higher dimensional solutions and the ones of one dimensional nonlinear Schrödinger equation with higher order nonlinearities is also discussed.
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