非线性晶格中呼吸子的随机共振成核

Klein-Gordon晶格中多位呼吸子的非线性不稳定性

Nonlinear instabilities of multi-site breathers in Klein-Gordon lattices

在目前的工作中，我们探讨的可能性激发呼吸状态的非线性Klein-Gordon晶格成为非线性不稳定，即使他们被发现是光谱稳定的。这种基本上非线性不稳定性的机制是通过与激发的呼吸状态的线性化中的内部模式本征频率的倍数的波连续体的共振。对于非线性不稳定性，内部模式必须具有与波连续体相反的Krein签名。这一机制不仅在理论上提出，而且还通过两个具体的例子的克莱因-戈登晶格与软（莫尔斯）和硬（$ϕ^4$）的潜力，数值证实。与非线性薛定谔晶格的情况相比，内部模式相对于波连续体的Krein签名可以根据激发呼吸态的周期而改变。对于Krein签名的内部模式和波的连续相吻合的时期，观察到激发呼吸状态是非线性稳定的。

Emergence and Ordering of Polygonal Breathers in Polariton Condensates

We show that the simultaneous driving of a polariton condensate with both nonresonant and n^th order resonant pump frequencies allows for a generic mechanism of breather formation; from this, we construct for the second-order resonance a family of exotic breathers with nontrivial discrete order of rotational symmetry. Finally, we demonstrate the spontaneous emergence of both crystalline and glassy orderings of lattices of polygonal breathers, depending on the degree of polygonal excitations at the lattice sites.

运动呼吸子与杂质的相互作用

Interaction of moving breathers with an impurity

分析了非弱非线性Klein-Gordon链中杂质对运动离散呼吸子演化的影响。当运动的呼吸与杂质相互作用时，可以观察到三种不同的行为：它们穿过杂质，继续它们的运动方向;它们被杂质反射;它们被杂质捕获，从而产生混乱的呼吸。与中心在杂质位置的呼吸器的共振被证明是捕获现象出现的必要条件。

Almost compact moving breathers with fine-tuned discrete time quantum walks

Discrete time quantum walks are unitary maps defined on the Hilbert space of coupled two-level systems. We study the dynamics of excitations in a nonlinear discrete time quantum walk, whose fine-tuned linear counterpart has a flat band structure. The linear counterpart is, therefore, lacking transport, with exact solutions being compactly localized. A solitary entity of the nonlinear walk moving at velocity $v$ would therefore not suffer from resonances with small amplitude plane waves with identical phase velocity, due to the absence of the latter. That solitary excitation would also have to …

离散非线性Schroedinger晶格中的q-呼吸子

q-breathers in Discrete Nonlinear Schroedinger lattices

$q$ -呼吸子是扩展非线性系统的精确时间周期解，它是由相应线性化系统的正常模式延续而来的。它们被局域化在简正模空间中。弱非谐原子链中这些解的存在解释了Fermi-Pasta-Ulam（FPU）佯谬的本质特征。我们研究了一维、二维和三维离散非线性薛定谔（DNLS）晶格中的$q$ -呼吸子--光在非线性光波导网络中传播的理论平台，以及光晶格中冷原子的动力学。我们证明了这些弱非线性解的存在性。我们发现，$q$ -呼吸子的局域化是由一个单一的参数，它取决于范数密度，非线性强度和种子波矢量。在该参数的临界值$q$ -呼吸离域通过共振，信号的正常模式图片的故障和过渡到强模式模式的相互作用制度。特别地，这种击穿发生在简正模谱的边缘之一处，并且以奇异的方式也发生在该谱的中心。$q$ -呼吸器的稳定性分析补充了这些发现。对于三维晶格，我们发现$q$呼吸旋涡，违反时间反演对称性，并产生一个涡环流的能量在正常模式空间。

非线性二聚体晶格的离散呼吸子：连接反连续极限与连续极限

Discrete Breathers of Nonlinear Dimer Lattices: Bridging the Anti-continuous and Continuous Limits

本文研究 SSH 非线性二聚体晶格中的离散呼吸子，证明弱耦合下存在周期、指数局域解，并通过矢量隙孤子包络理论连接反连续与连续极限，数值验证一致。

Multistable Dissipative Breathers and Novel Collective States in SQUID Lieb Metamaterials

A SQUID (Superconducting QUantum Interference Device) metamaterial on a Lieb lattice with nearest-neighbor coupling supports simultaneously stable dissipative breather families which are generated through a delicate balance of input power and intrinsic losses. Breather multistability is possible due to the peculiar snaking flux ampitude - frequency curve of single dissipative-driven SQUIDs, which for relatively high sinusoidal flux field amplitudes exhibits several stable and unstable solutions in a narrow frequency band around resonance. These breathers are very weakly interacting with each o…

约瑟夫森阶梯中的离散呼吸子

Discrete Breathers in Josephson Ladders

我们提出了一个研究的非线性局域激发称为离散呼吸子在超导阵列。这些本地化的解决方案，最近观察到约瑟夫森结梯形阵列由两个不同的实验组。我们回顾了Trias等人的实验。我们报告了不同的单站点和多站点呼吸状态的检测，并研究了改变阵列偏置电流时的动态。通过改变温度，我们可以控制阵列中的阻尼值（Stewart-McCumber参数），从而允许在不同的阵列参数下进行实验研究。我们提出了一个简单的直流电路模型，以了解检测状态的大部分功能。我们还比较了这个模型和实验与模拟的动态阵列。我们表明，在阶梯的谐振和使用谐波平衡技术的研究允许理解的大部分数值结果。我们已经计算了我们的阵列呼吸解决方案的存在图，发现共振本地化的解决方案和描述的本地化状态的涡旋和antivortex运动。

Fermi-Pasta-Ulam晶格中的离散呼吸子

Discrete breathers in Fermi-Pasta-Ulam lattices

Fermi-Pasta-Ulam（FPU）悖论在50年前被发现。令人惊讶的发现是一个本地化的能量在倒数q空间的离散平移不变性的模型，尽管存在的扩展正常模式之间的相互作用。33年后，Takeno，Kisoda和Sievers报道了在实空间中观察到的能量局域化，这是令人惊讶的，因为这些激发，称为离散呼吸子或固有局域模式，违反了模型的基本离散平移对称性。近十年来，离散呼吸子的理论和应用取得了巨大的进展，远远超出了最初的FPU框架的范围。我们使用现代离散呼吸子理论来研究FPU模型中这些解的性质，特别注意稳定性、共振、波散射和能量阈值等问题。

具有长程、非凸色散介质中的亮传播呼吸子

Bright traveling breathers in media with long-range, nonconvex dispersion

本文数值研究了非局域色散介质中亮传播呼吸子的存在与性质，通过求解Benjamin-Bona-Mahony方程和conduit方程，揭示了非凸色散导致的振荡背景及拓扑相位跳跃现象，为海洋内波和光脉冲等系统提供了理论见解。

Heteroclinic structure of parametric resonance in the nonlinear Schrödinger equation

We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schrödinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric ampl…

超谐共振下阻尼非线性无序超结构的能量局域化

Energy localization in damped nonlinear disordered metastructures under superharmonic resonance

提出非基谐共振下非线性振子链能量局域化框架，利用多尺度法导出孤子动力学方程，揭示超谐共振中相位的关键作用，并评估无序鲁棒性。

Two-dimensional nonlinear modes and frequency combs in bottle microresonators

We investigate theoretically frequency comb generation in a bottle microresonator accounting for the azimuthal and axial degrees of freedom. We first identify a discrete set of the axial nonlinear modes of a bottle microresonator that appear as tilted resonances bifurcating from the spectrum of linear axial modes. We then study azimuthal modulational instability of these modes and show that families of 2D soliton states localized both azimuthally and axially bifurcate from them at critical pump frequencies. Depending on detuning, 2D solitons can be either stable, or form persistent breathers, …