论文标题
具有深晶格的非线性分数系统中的局部模式
Localized modes in nonlinear fractional systems with deep lattices
论文作者
论文摘要
由格子电位支持的分数空间中的孤子最近引起了人们的极大兴趣。我们考虑该系统中深一维（1d和2d）晶格的极限，其特征是几乎平坦的Bloch频段分隔的有限带盖。在当前的研究中，这种光谱也是引起人们关注的主题。通过数值方法研究了各种局部模式的存在，形状和稳定性，包括基本间隙和涡流孤子。在分析近似值的帮助下，还获得了一些结果。特别是，属于第一和第二有限带盖的1D和2D间隙孤子密切限制在深晶格的单个单元格周围。涡旋差距孤子构建为四峰\ togequotedblleft方块“和\ textquotedblleft菱形”，上面有刻有缠绕的数字$ s = 1 $。通过线性化探索孤子的稳定性，并通过直接模拟进行验证。
Solitons in the fractional space, supported by lattice potentials, have recently attracted much interest. We consider the limit of deep one- and two-dimensional (1D and 2D) lattices in this system, featuring finite bandgaps separated by nearly flat Bloch bands. Such spectra are also a subject of great interest in current studies. The existence, shapes, and stability of various localized modes, including fundamental gap and vortex solitons, are investigated by means of numerical methods; some results are also obtained with the help of analytical approximations. In particular, the 1D and 2D gap solitons, belonging to the first and second finite bandgaps, are tightly confined around a single cell of the deep lattice. Vortex gap solitons are constructed as four-peak \textquotedblleft squares" and \textquotedblleft rhombuses" with imprinted winding number $S=1$. Stability of the solitons is explored by means of the linearization and verified by direct simulations.
