蜂窝晶格近半狄拉克点处的离散呼吸子
Discrete Breathers in a Honeycomb Lattice Near a Semi-Dirac Point
AI总结：
研究非线性蜂窝晶格中近半狄拉克点处离散呼吸子的动力学，揭示其稳定性特征及在带隙内的结构形成机制。
摘要：
我们研究了非线性蜂窝晶格带隙内离散呼吸子的动力学，这些呼吸子是空间局域且时间周期性的解。在该晶格中，色散图谱接近所谓的半狄拉克点，其中在某一方向上色带线性交叉，在垂直方向上二次交叉。通过研究呼吸子在两个对立的渐近极限附近（即连续极限和反连续极限）的动力学，我们捕捉到在晶格中高度离散的混合相干结构，其呼吸子中心峰值高度离散，而尾部可近似为有效长波PDE理论的精确分离解。我们发现呼吸子在广泛参数范围内动态稳定，并确定了不稳定性转变点。最后，我们分析了从零解边缘处 bifurcating 出来的非线性平面波的傅里叶稳定性，以及这些波如何塑造晶格带隙内的呼吸子轮廓。
英文摘要：
We study the dynamics of discrete breathers---spatially localized and time-periodic solutions---inside the bandgap of a nonlinear honeycomb lattice where the dispersion landscape approaches a so-called semi-Dirac point in which the bands cross linearly in one direction and quadratically in the orthogonal direction. By studying breather dynamics in two opposing asymptotic regimes, near the continuum and anti-continuum limits, we capture the spatial profiles of hybrid coherent structures having central cores supported on a finite number of lattice sites and infinite decaying tails that are well approximated by exact separable solutions to an effective long-wave PDE theory at spatial infinity. We find that these breathers are dynamically stable over a wide range of parameters and find an instability transition. Finally, we analyze the Floquet stability of spatially extended nonlinear plane waves bifurcating from the zero solution at the edges of the gap and how they shape breather profiles inside the gap.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
