论文标题
二维正弦格式方程的通气条纹和径向呼吸器
Breather stripes and radial breathers of the two-dimensional sine-Gordon equation
论文作者
论文摘要
我们重新审视正弦 - 戈登方程（SG）方程的2D呼吸条纹的横向不稳定性问题。将条纹的数值计算的浮子光谱与通过多尺度扰动理论开发的分析预测进行了比较，该预测在长波长极限下显示出良好的一致性。通过直接的模拟，发现不稳定性导致一系列相互作用的2D径向呼吸器的准1D呼吸器破裂，这些呼吸器在动力学中似乎相当强大。通过数值方法详细研究了有限域中径向呼吸器的稳定性和动力学。确定了这种解决方案的不同家庭。他们通过与属于连续光谱的线性模式（“ Phonon”）的高阶呼吸器的谐波共鸣，在空间上振荡的尾巴（“纳米翅目”）形成了小振幅。这些结果证明了2D SG模型在我们的有限域计算中将能量定位在长寿，自被捕的呼吸激发中的能力。
We revisit the problem of transverse instability of a 2D breather stripe of the sine-Gordon (sG) equation. A numerically computed Floquet spectrum of the stripe is compared to analytical predictions developed by means of multiple-scale perturbation theory showing good agreement in the long-wavelength limit. By means of direct simulations, it is found that the instability leads to a breakup of the quasi-1D breather in a chain of interacting 2D radial breathers that appear to be fairly robust in the dynamics. The stability and dynamics of radial breathers in a finite domain are studied in detail by means of numerical methods. Different families of such solutions are identified. They develop small-amplitude spatially oscillating tails ("nanoptera") through a resonance of higher-order breather's harmonics with linear modes ("phonons") belonging to the continuous spectrum. These results demonstrate the ability of the 2D sG model within our finite domain computations to localize energy in long-lived, self-trapped breathing excitations.
