Solitons in the discrete nonpolynomial Schrödinger equation
Solitons in the discrete nonpolynomial Schrödinger equation
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DOI：
10.1103/physreva.78.013616
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发表时间：
2008-07
影响因子：
2.9
通讯作者：
A. Maluckov;L. Hadzievski;B. Malomed;L. Salasnich
中科院分区：
文献类型：
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作者：
A. Maluckov;L. Hadzievski;B. Malomed;L. Salasnich
我们引入了一种离散非线性Schrödinger （DNLS）方程，它是一个自吸引玻色-爱因斯坦凝聚体的模型，它被限制在雪茄形阱和深光学晶格的组合中，作用于轴向。该方程推导为各自非线性非多项式Schrödinger方程的离散化。与以前考虑的一维DNLS方程不同，目前的离散模型允许现场坍塌。我们找到了稳定孤子和不稳定孤子两族，它们分别包括广义孤子和狭义孤子，它们的稳定性完全符合Vakhitov-Kolokolov判据。不稳定的现场孤子要么衰变，要么转变为强健的呼吸体。以点间为中心的非交错孤子不稳定，容易坍塌；然而，它们可以通过应用足够强的踢腿来稳定，从而使它们变成移动的局部模式。通过将井涌应用于稳定的现场非交错孤子，也可以很容易地创建持续移动的孤子。在同一模型中，如果本征非线性是自排斥的，则可能存在与连续介质中的间隙孤子对应的交错孤子。所有场址交错孤子都是稳定的，而场址间的交错孤子有一个小的不稳定区。交错的孤子是不动的。
We introduce a species of the discrete nonlinear Schrödinger (DNLS) equation, which is a model for a self-attractive Bose-Einstein condensate confined in a combination of a cigar-shaped trap and deep optical lattice acting in the axial direction. The equation is derived as a discretization of the respective nonlinear nonpolynomial Schrödinger equation. Unlike previously considered varieties of one-dimensional DNLS equations, the present discrete model admits on-site collapse. We find two families of unstaggered on-site-centered discrete solitons, stable and unstable ones, which include, respectively, broad and narrow solitons, their stability exactly complying with the Vakhitov-Kolokolov criterion. Unstable on-site solitons either decay or transform themselves into robust breathers. Intersite-centered unstaggered solitons are unstable to collapse; however, they may be stabilized by the application of a sufficiently strong kick, which turns them into moving localized modes. Persistently moving solitons can be readily created too by the application of the kick to stable on-site unstaggered solitons. In the same model, staggered solitons, which are counterparts of gap solitons in the continuum medium, are possible if the intrinsic nonlinearity is self-repulsive. All on-site staggered solitons are stable, while intersite ones have a small instability region. The staggered solitons are immobile.