论文标题
$β$ -Fermi-pasta-pasta-ulam-tsingou二聚体晶格中的狄拉克孤子和拓扑边缘状态
Dirac Solitons and Topological Edge States in the $β$-Fermi-Pasta-Ulam-Tsingou dimer lattice
论文作者
论文摘要
我们考虑Fermi-Pasta-ulam-tsingou（fput）类型的二聚体晶格，其中交替的线性耦合具有很小的差异，并且对于所有相互作用对而言，立方非线性（$β$ -FPUT）都是相同的。我们在晶格带隙内使用弱非线性正式还原，以获得连续的非线性狄拉克型系统。我们通过分析得出Dirac soliton概况和模型的保护定律。然后，我们检查了半无限和有限域的情况，并说明了批量问题的孤子解决方案如何``粘合''到不同类型的边界条件的边界上。因此，我们解释了系统中各种非线性边缘状态的存在，其中只有一个导致在线性极限中观察到的标准拓扑边缘状态。我们最终检查了散装和边缘状态的稳定性，并通过直接数值模拟对它们进行验证，在这种模拟中，我们观察到由于不稳定性而导致的孤立波动。
We consider a dimer lattice of the Fermi-Pasta-Ulam-Tsingou (FPUT) type, where alternating linear couplings have a controllably small difference, and the cubic nonlinearity ($β$-FPUT) is the same for all interaction pairs. We use a weakly nonlinear formal reduction within the lattice bandgap to obtain a continuum, nonlinear Dirac-type system. We derive the Dirac soliton profiles and the model's conservation laws analytically. We then examine the cases of the semi-infinite and the finite domains and illustrate how the soliton solutions of the bulk problem can be ``glued'' to the boundaries for different types of boundary conditions. We thus explain the existence of various kinds of nonlinear edge states in the system, of which only one leads to the standard topological edge states observed in the linear limit. We finally examine the stability of bulk and edge states and verify them through direct numerical simulations, in which we observe a solitary wave setting into motion due to the instability.
