论文标题
分散型Swift-Hohenberg方程产生的空间扩展位错
Spatially Extended Dislocations Produced by the Dispersive Swift-Hohenberg Equation
论文作者
论文摘要
先前的结果激励表明，在二维kuramoto-sivashinsky方程中添加线性分散项对模式形成具有巨大的影响，我们研究了Swift-Hohenberg方程，并增加了线性分散项，分散性Swift Swift-Hohenberg方程（DSHE）。 DSHE产生带有空间扩展位错的条纹模式，我们称为接缝缺陷。与色散的库拉莫托 - 摩托岛方程相反，DSHE的波长狭窄，接近不稳定性阈值。这样可以取得分析进度。我们表明，DSHE接近阈值的振幅方程是各向异性复合物Ginzburg-Landau方程（ACGLE）的特殊情况，并且DSHE中的接缝对应于Acgle中的螺旋波。接缝缺陷和相应的螺旋波倾向于将自己组织成链，我们获得了螺旋波芯速度以及它们之间的间距的公式。在强分散的极限下，扰动分析产生条带模式的幅度和波长之间的关系及其传播速度。 Acgle和DSHE的数值整合确认了这些分析结果。
Motivated by previous results showing that the addition of a linear dispersive term to the two-dimensional Kuramoto-Sivashinsky equation has a dramatic effect on the pattern formation, we study the Swift-Hohenberg equation with an added linear dispersive term, the dispersive Swift-Hohenberg equation (DSHE). The DSHE produces stripe patterns with spatially extended dislocations that we call seam defects. In contrast to the dispersive Kuramoto-Sivashinsky equation, the DSHE has a narrow band of unstable wavelengths close to an instability threshold. This allows for analytical progress to be made. We show that the amplitude equation for the DSHE close to threshold is a special case of the anisotropic complex Ginzburg-Landau equation (ACGLE) and that seams in the DSHE correspond to spiral waves in the ACGLE. Seam defects and the corresponding spiral waves tend to organize themselves into chains, and we obtain formulas for the velocity of the spiral wave cores and for the spacing between them. In the limit of strong dispersion, a perturbative analysis yields a relationship between the amplitude and wavelength of a stripe pattern and its propagation velocity. Numerical integrations of the ACGLE and the DSHE confirm these analytical results.
