参数驱动非线性谐振器阵列的方向图选择

optical fiber环形非线性谐振腔中的参量模式

Parametric patterns in optical fiber ring nonlinear resonators

我们提出在非线性光纤谐振腔中可以观察到参数激励模式，也称为法拉第模式，其中克尔非线性系数沿谐振腔中的光纤周期性变化。我们研究的参数不稳定性分析的Floquet理论的基础上，也数值，通过直接集成的系统。而不是经典的法拉第波激发的情况下，在时间上的调制导致在空间中的图案的形成，在这里，我们提出了一个反转的情况下，在空间中的调制激发的图案在时间上。

Two-dimensional optical chimera states in an array of coupled waveguide resonators

Two-dimensional arrays of coupled waveguides or coupled microcavities allow to confine and manipulate light. Based on a paradigmatic envelope equation, we show that these devices, subject to a coherent optical injection, support coexistence between a coherent and incoherent emission. In this regime, we show that two-dimensional chimera state can be generated. Depending on initial conditions, the system exhibits a family of two-dimensional chimera states and interaction between them. We characterize these two-dimensional structures by computing their Lyapunov spectrum, and Yorke-Kaplan dimensio…

Generation and propagation of topological solitons in a chain of coupled parametric-micromechanical-resonator arrays

Using a coupled parametric-resonator array for generating and propagating a topological soliton in its rotating-frame phase space is theoretically and numerically investigated. In an analogy with the well-known phi4 model, the existence of a soliton is topologically protected as the boundary of two different phase domains of parametric oscillation. Numerical simulation indicates that the propagation can be triggered by switching of the phase state of one specific resonator, and the effects of damping, collision, and the symmetry lifting by harmonic drive on the propagation dynamics are studied…

耦合非线性谐振腔阵列中的集体动力学

Collective Dynamics in Arrays of Coupled Nonlinear Resonators

近年来，由于微机电和纳机电系统（MEMS和NEMS）领域的快速发展，耦合机械谐振器的集体非线性动力学的研究重新受到关注。我们回顾了广泛的集体动力学现象，同时强调了共同的概念和理论工具，我们已经开发了治疗它们。我们提供了详细的推导振幅方程，这使我们能够获得减少我们的复杂系统的相关动态的描述。我们应用这些振幅方程来研究（a）共振响应参数激励;（b）模式选择，或扩展模式之间的非线性竞争的情况下的多稳定性;（c）形成和动力学的固有局域模式（ILM）;和（d）自发同步的振荡器具有不同的频率。从分析不同的振幅方程得到的所有预测与基本运动方程的数值解非常一致，这表明预测的效果可以在真实的微机械或纳米机械谐振器阵列中观察到，从而激发了这些系统中的新实验。

机电谐振腔中的离散孤子

Discrete solitons in electromechanical resonators

我们考虑一个参数驱动的克莱因-戈登系统描述微和纳米器件，集成的电气和机械功能。利用多尺度展开方法，我们减少了系统的离散非线性薛定谔方程。通过离散薛定谔方程，分析和数值计算了Klein-Gordon系统中基本离散亮孤子和暗孤子的存在性和稳定性.结果表明，参量驱动不仅可以使场内亮孤子不稳定，而且可以使场间离散亮孤子以及场内和场间暗孤子稳定。最重要的是，我们表明，有一个范围内的驱动系数的值，暗孤子是稳定的，对于任何值的耦合常数，即振荡不稳定性完全抑制。所有的基本孤子的稳定性窗口和近似的发病不稳定性的微扰理论推导，伴随的数值结果。数值积分的Klein-Gordon方程进行，确认我们的分析的相关性。

Justification of the discrete nonlinear Schrödinger equation from a parametrically driven damped nonlinear Klein-Gordon equation and numerical comparisons

We consider a damped, parametrically driven discrete nonlinear Klein-Gordon equation, that models coupled pendula and micromechanical arrays, among others. To study the equation, one usually uses a small-amplitude wave ansatz, that reduces the equation into a discrete nonlinear Schrödinger equation with damping and parametric drive. Here, we justify the approximation by looking for the error bound with the method of energy estimates. Furthermore, we prove the local and global existence of {solutions to the discrete nonlinear} Schrödinger equation. To illustrate the main results, we consider nu…