标题： 一维非线性晶格中的离散嵌入孤立波和呼吸子 显示英文标题

标题： Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices

摘要： 对于一维线性晶格，早期的研究已经展示如何系统地构造一个缓慢衰减的线性势，该势具有嵌入连续谱中的局域化本征模态。 在这里，我们从两个方向扩展了这一思想：第一个方向是在离散非线性薛定谔方程的领域中，其中在存在克尔聚焦或非聚焦非线性的情况下考虑了薛定谔类型的线性算子，并且嵌入的线性模态在非线性区域中继续作为离散孤子波存在。 第二个情况是克莱因-戈登设置，在这种情况下，三次非线性导致嵌入连续谱中的离散呼吸子的出现。 在两种情况下，都观察到在非线性超过临界值后，靠近线性极限的模态的稳定性转变为不稳定性，导致孤子波（或振动）状态的动力学去局域化。 最后，我们建议了一个具体的实验，使用双感应电气晶格来观察这些嵌入模态。 显示英文摘要

摘要： For a one-dimensional linear lattice, earlier work has shown how to systematically construct a slowly-decaying linear potential bearing a localized eigenmode embedded in the continuous spectrum. Here, we extend this idea in two directions: The first one is in the realm of the discrete nonlinear Schrodinger equation, where the linear operator of the Schrodinger type is considered in the presence of a Kerr focusing or defocusing nonlinearity and the embedded linear mode is continued into the nonlinear regime as a discrete solitary wave. The second case is the Klein-Gordon setting, where the presence of a cubic nonlinearity leads to the emergence of embedded-in-the-continuum discrete breathers. In both settings, it is seen that the stability of the modes near the linear limit turns into instability as nonlinearity is increased past a critical value, leading to a dynamical delocalization of the solitary wave (or breathing) state. Finally, we suggest a concrete experiment to observe these embedded modes using a bi-inductive electrical lattice.