强迫阻尼耦合摆阵中的离散呼吸子：建模、计算和实验

Breathers in Hamiltonian ${\cal PT}$-symmetric chains of coupled pendula under a resonant periodic force

We derive a Hamiltonian version of the ${\cal PT}$-symmetric discrete nonlinear Schrödinger equation that describes synchronized dynamics of coupled pendula driven by a periodic movement of their common strings. In the limit of weak coupling between the pendula, we classify the existence and spectral stability of breathers (time-periodic solutions localized in the lattice) supported near one pair of coupled pendula. Orbital stability or instability of breathers is proved in a subset of the existence region.

Long-time stability of breathers in Hamiltonian $\cal PT$-symmetric lattices

We consider the Hamiltonian version of a $\cal PT$-symmetric lattice that describes dynamics of coupled pendula under a resonant periodic force. Using the asymptotic limit of a weak coupling between the pendula, we prove the nonlinear long-time stability of breathers (time-periodic solutions localized in the lattice) by using the Lyapunov method. Breathers are saddle points of the extended energy function, which are located between the continuous bands of positive and negative energy. Nevertheless, we construct an approximate Lyapunov function and estimate its evolution on a long but finite ti…

Multifrequency and edge breathers in the discrete sine-Gordon system via subharmonic driving: theory, computation and experiment

We consider a chain of torsionally-coupled, planar pendula shaken horizontally by an external sinusoidal driver. It has been known that in such a system, theoretically modeled by the discrete sine-Gordon equation, intrinsic localized modes, also known as discrete breathers, can exist. Recently, the existence of multifrequency breathers via subharmonic driving has been theoretically proposed and numerically illustrated by Xu {\em et al.} in Phys. Rev. E {\bf 90}, 042921 (2014). In this paper, we verify this prediction experimentally. Comparison of the experimental results to numerical simulatio…

Exact solutions for discrete breathers in forced-damped chain

Exact solutions for symmetric discrete breathers (DBs) are obtained in forced-damped linear chain with on-site vibro-impact constraints. The damping is related to inelastic impacts; the forcing may be chosen from broad class of periodic antisymmetric functions. Global conditions for existence and stability of the DB are established. Some unusual phenomena, like non-monotonous dependence of the stability boundary on the forcing amplitude, are revealed analytically for the full system and illustrated numerically for small periodic lattices.

Amplification of wave groups in the forced nonlinear Schrödinger equation

In many physical contexts, notably including deep water waves, modulation instability in one space dimension is often studied using the nonlinear Schrödinger equation. The principal solutions of interest are solitons and breathers which are adopted as models of wave packets. The Peregrine breather in particular is often invoked as a model of a rogue wave. In this paper we add a linear growth term to the nonlinear Schrödinger equation to model the amplification of propagating wave groups. This is motivated by an application to wind-generated water waves, but this forced nonlinear Schrödinger eq…

移动式分立呼吸器的锁模

Mode-Locking of mobile discrete breathers

研究了周期性强迫下耗散非线性晶格中运动离散呼吸子的同步现象。当改变驱动强度时，呼吸器速度通常锁定在驱动频率的有理数倍。在大多数情况下，锁定平台与共振移动呼吸器的线性稳定域相一致，并且通过定期出现I型呼吸器来发生去极化。然而，一些高原也显示了混沌的移动呼吸子锁定速度的锁定区域。小的次谐波驱动驯服锁定的混沌解，提高了共振移动呼吸子的稳定性。