论文标题
与交替应变硬化和压力互动的晶格中的呼吸器
Breathers in lattices with alternating strain-hardening and strain-softening interactions
论文作者
论文摘要
这项工作重点是在非线性晶格中的时间周期溶液（包括呼吸器）的研究，该晶格由元素组成，其元素的元素在菌株硬化和舒适度之间进行交替。系统地研究了这种解决方案的存在，稳定性和分叉结构，以及在阻尼和驾驶存在下的系统动力学。发现在非线性存在下，系统中的线性谐振峰朝向频率间隙弯曲。如果阻尼和驾驶很小，则在频率差距内的时间周期性解决方案与哈密顿呼吸器相比良好。在问题的哈密顿限制中，我们使用多个量表分析来得出非线性Schrödinger（NLS）方程来构建声学和光学呼吸器。后者与在哈密顿限制中获得的数值获得的呼吸器相比非常好。
This work focuses on the study of time-periodic solutions, including breathers, in a nonlinear lattice consisting of elements whose contacts alternate between strain-hardening and strain-softening. The existence, stability, and bifurcation structure of such solutions, as well as the system dynamics in the presence of damping and driving are studied systematically. It is found that the linear resonant peaks in the system bend toward the frequency gap in the presence of nonlinearity. The time-periodic solutions that lie within the frequency gap compare well to Hamiltonian breathers if the damping and driving are small. In the Hamiltonian limit of the problem, we use a multiple scale analysis to derive a Nonlinear Schrödinger (NLS) equation to construct both acoustic and optical breathers. The latter compare very well with the numerically obtained breathers in the Hamiltonian limit.
