论文标题
紧凑型呼吸器的稳定性在翻译不变的非线性链中具有平坦色散带的稳定性
Stability of compact breathers in translationally-invariant nonlinear chains with flat dispersion bands
论文作者
论文摘要
本文以平坦的晶格介绍了带有平坦分散带的翻译不变晶格中的紧凑型振荡状态（紧凑的呼吸器）。即使在线性近似中，紧凑的呼吸器也会出现在这样的系统中。如果相互作用是非线性的，但符合平坦的对称性，则存在紧凑的呼吸溶液，但可能会失去某些参数值的稳定性。作为基准非线性电位，我们使用$β$ -FPU（Fermi-Pasta-ulam）和振动障碍模型。从数值上观察到稳定性的丧失是通过干草叉或霍夫夫分叉发生的。稳定性的丧失可以通过两种定性不同的机制发生 - 通过基本晶格元件中的内部不稳定性，或通过紧凑的呼吸与晶格的线性通带相互作用。对于高振幅呼吸器而言，前一种情况更为典型，而后者则是低振幅的。对于高振幅案例，通过诉诸于分段线性系统的极限来获得对紧凑型稳定性损失性质的见解，在该系统中，相互作用由保守的影响表示。本期要求详细的内省性内置性（影响）系统的整合性及其与平滑系统的关系。提出了基于研究机制的传感器的想法。
The paper addresses compact oscillatory states (compact breathers) in translationally-invariant lattices with flat dispersion bands. The compact breathers appear in such systems even in the linear approximation. If the interactions are nonlinear, but comply with the flat-band symmetry, the compact breather solutions exist, but can lose their stability for certain parameter values. As benchmark nonlinear potentials, we use the $β$-FPU (Fermi-Pasta-Ulam) and vibro-impact models. Loss of stability is numerically observed to occur through either pitchfork or Hopf bifurcations. The loss of stability can occur through two qualitatively different mechanisms -- through internal instability in the basic lattice elements, or through interaction of the compact breather with the linear passband of the lattice. The former scenario is more typical for high-amplitude breathers, and the latter -- for low amplitudes. For the high-amplitude case, insights into the nature of compact-mode loss-of-stability are obtained by resorting to the limit of a piecewise-linear system, where interactions are represented by conservative impacts. This issue calls for detailed introspection into integrability of piecewise-linear (impacting) systems and their relation to the smooth system. An idea for a sensor based on the studied mechanisms is suggested.
