Alexander T J, Yan D, Kevrekidis P G
School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, Australia 2600.
Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Dec;88(6):062908. doi: 10.1103/PhysRevE.88.062908. Epub 2013 Dec 4.
We explore how nonlinear coherent waves localized in a few wells of a periodic potential can act analogously to a chain of coupled oscillators. We identify the small-amplitude oscillation modes of these "coupled wave oscillators" and find that they can be extended into the large amplitude regime, where some "ring" for long times. We also reveal the appearance of complex behavior such as the breakdown of Josephson-like oscillations, the destabilization of fundamental oscillation modes, and the emergence of chaotic oscillations for large amplitude excitations. We show that the dynamics may be accurately described by a discrete model with nearest-neighbor coupling, in which the lattice oscillators bear an effective mass.
我们探究了局域在周期势几个阱中的非线性相干波如何能类似于耦合振子链那样起作用。我们确定了这些“耦合波振子”的小振幅振荡模式，并发现它们能扩展到大振幅区域，在该区域一些会长时间“环绕”。我们还揭示了复杂行为的出现，比如类约瑟夫森振荡的崩溃、基本振荡模式的失稳以及大振幅激发时混沌振荡的出现。我们表明，动力学可以由具有最近邻耦合的离散模型精确描述，其中晶格振子具有有效质量。
