论文标题
蛇在lieb晶格上
Snakes on Lieb lattice
论文作者
论文摘要
我们考虑了Lieb晶格上具有立方体和五分之性非线性的离散的Allen-CAHN方程。我们研究了系统的局部非线性溶液，它们的分叉图中具有线性多稳定性和磁滞。在这项工作中，我们研究了系统的同型蛇，即分叉图的蛇形结构，尤其是晶格类型的效果。使用伪长方法的数值延续用于沿分叉图获得局部解决方案。然后，我们开发一个主动细胞近似，以分类转弯点的解决方案类型，当站点弱耦合时，该近似与数值结果很好地一致。还讨论了固定区域内外的局部解决方案的时间动力学。
We consider the discrete Allen-Cahn equation with cubic and quintic nonlinearity on the Lieb lattice. We study localized nonlinear solutions of the system that have linear multistability and hysteresis in their bifurcation diagram. In this work, we investigate the system's homoclinic snaking, i.e. snaking-like structure of the bifurcation diagram, particularly the effect of the lattice type. Numerical continuation using a pseudoarclength method is used to obtain localized solutions along the bifurcation diagram. We then develop an active-cell approximation to classify the type of solution at the turning points, which gives good agreement with the numerical results when the sites are weakly coupled. Time dynamics of localized solutions inside and outside the pinning region is also discussed.
