Damped and driven breathers and metastability
Damped and driven breathers and metastability
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DOI：
10.1090/qam/1650
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发表时间：
2021-01
影响因子：
0.8
通讯作者：
Daniel A. Caballero;C. E. Wayne
中科院分区：
文献类型：
--
作者：
Daniel A. Caballero;C. E. Wayne
在这篇文章中，我们证明了一族新的周期解的离散，非线性薛定谔方程的空间局部驱动和阻尼。他们提供了一个替代的描述，在这样的晶格系统，同意与以前的预测亚稳态的演变，同时提供更准确的近似这些国家的亚稳态行为。我们分析了这些呼吸器的稳定性，发现一个非常小的正特征值，其特征向量几乎相切于呼吸器的家庭所形成的圆柱体的表面。这会导致溶液沿圆柱体沿着滑动，而不会离开其邻域很长时间。
In this article we prove the existence of a new family of periodic solutions for discrete, nonlinear Schrödinger equations subject to spatially localized driving and damping. They provide an alternate description of the metastable behavior in such lattice systems which agrees with previous predictions for the evolution of metastable states while providing more accurate approximations to these states. We analyze the stability of these breathers, finding a very small positive eigenvalue whose eigenvector lies almost tangent to the surface of the cylinder formed by the family of breathers. This causes solutions to slide along the cylinder without leaving its neighborhood for very long times.