Kevrekidis P G, Carretero-González R, Frantzeskakis D J, Malomed B A, Diakonos F K
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Feb;75(2 Pt 2):026603. doi: 10.1103/PhysRevE.75.026603. Epub 2007 Feb 8.
We construct, in discrete two-component systems with cubic nonlinearity, stable states emulating Skyrmions of the classical field theory. In the two-dimensional case, an analog of the baby Skyrmion is built on the square lattice as a discrete vortex soliton of a complex field [whose vorticity plays the role of the Skyrmion's winding number (WN)], coupled to a radial "bubble" in a real lattice field. The most compact quasi-Skyrmion on the cubic lattice is composed of a nearly planar complex-field discrete vortex and a three-dimensional real-field bubble; unlike its continuum counterpart which must have WN=2, this stable discrete state exists with WN=1. Analogs of Skyrmions in the one-dimensional lattice are also constructed. Stability regions for all these states are found in an analytical approximation and verified numerically. The dynamics of unstable discrete Skyrmions (which leads to the onset of lattice turbulence) and their partial stabilization by external potentials are explored too.
我们在具有立方非线性的离散双组分系统中构建了模拟经典场论中斯格明子的稳定态。在二维情况下，婴儿斯格明子的类似物被构建在正方形晶格上，作为复场的离散涡旋孤子（其涡度起着斯格明子缠绕数（WN）的作用），与实晶格场中的径向“气泡”耦合。立方晶格上最紧凑的准斯格明子由一个近乎平面的复场离散涡旋和一个三维实场气泡组成；与连续介质中对应物必须具有WN = 2不同，这种稳定的离散态以WN = 1存在。还构建了一维晶格中斯格明子的类似物。通过解析近似找到了所有这些态的稳定区域，并进行了数值验证。还探索了不稳定离散斯格明子的动力学（这导致晶格湍流的开始）以及它们通过外部势的部分稳定化。
