Asymptotics of large bound states of localized structures.
Asymptotics of large bound states of localized structures.
复制标题
局域结构大束缚态的渐近。
DOI：
10.1103/physrevlett.97.044502
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发表时间：
2006
影响因子：
8.6
通讯作者：
Stephen Chapman
中科院分区：
文献类型：
--
作者：
G. Kozyreff;Stephen Chapman
我们分析了连接均匀状态和周期性状态的静止锋，这些状态是从形成模式的不稳定性中出现的。所产生的周期域的大小无法用弱非线性方法来预测。我们证明，决定这个大小的因素是指数小（但在空间上呈指数增长）的项。这些只能通过超越通常的多尺度展开的所有阶数来计算。我们将该方法应用于 Swift-Hohenberg 方程，并解析得出一条蛇形分岔曲线。在此分叉曲线的每次折叠处，周期域中都会添加一对新峰，因此可以将其视为局部结构的束缚态。已经报道了非线性腔中的光学局部结构和局部屈曲的这种情况。
We analyze stationary fronts connecting uniform and periodic states emerging from a pattern-forming instability. The size of the resulting periodic domains cannot be predicted with weakly nonlinear methods. We show that what determine this size are exponentially small (but exponentially growing in space) terms. These can only be computed by going beyond all orders of the usual multiple-scale expansion. We apply the method to the Swift-Hohenberg equation and derive analytically a snaking bifurcation curve. At each fold of this bifurcation curve, a new pair of peaks is added to the periodic domain, which can thus be seen as a bound state of localized structures. Such scenarios have been reported with optical localized structures in nonlinear cavities and localized buckling.