论文标题
在广义的迅速中的局部模式 - 霍恩伯格方程，具有四分之一的边缘稳定性曲线
Localised patterns in a generalised Swift--Hohenberg equation with a quartic marginal stability curve
论文作者
论文摘要
在某些模式形成系统中，对于某些参数值，形成了具有两个波长的模式，而对于其他参数值，只有一个波长。这些之间的过渡可以通过一个编的三个点来组织，该点的边缘稳定曲线具有四分之一的最小值。我们开发了一个模型方程，以基于Swift-Hohenberg方程来探索这种情况；该模型除其他外，还包含一个位于另一个波长模式背景的一个波长的图案的分支。在小振幅极限中，该模型的振幅方程是具有四阶空间衍生物的广义的金茨堡 - landau方程，它可以采用具有实际系数的复杂swift-hohenberg方程的形式。该幅度方程中的局部解决方案有助于解释模型中的局部模式。这项工作扩展了最新的努力，以调查模式形成系统中的蛇纹行为，在同一参数值中存在两个不同稳定的非平凡模式。
In some pattern-forming systems, for some parameter values, patterns form with two wavelengths, while for other parameter values, there is only one wavelength. The transition between these can be organised by a codimension-three point at which the marginal stability curve has a quartic minimum. We develop a model equation to explore this situation, based on the Swift--Hohenberg equation; the model contains, amongst other things, snaking branches of patterns of one wavelength localised in a background of patterns of another wavelength. In the small-amplitude limit, the amplitude equation for the model is a generalised Ginzburg--Landau equation with fourth-order spatial derivatives, which can take the form of a complex Swift--Hohenberg equation with real coefficients. Localised solutions in this amplitude equation help interpret the localised patterns in the model. This work extends recent efforts to investigate snaking behaviour in pattern-forming systems where two different stable non-trivial patterns exist at the same parameter values.
