Pattern Formation in Systems with Slowly Varying Geometry
Pattern Formation in Systems with Slowly Varying Geometry
复制标题
几何形状缓慢变化的系统中的图案形成
DOI：
--
复制
发表时间：
1997
影响因子：
1.9
通讯作者：
W. Eckhaus
中科院分区：
文献类型：
--
作者：
R. Kuske;W. Eckhaus
考虑了一类方程，它描述了具有小参数$ilde的几何略微变化的问题中图案的演化
ULL 1$，慢慢地，在空间尺度上，$hatepsilon x$代表$hatepsilonll 1$。该模型受蜿蜒河流泥沙问题的启发，被推广到一个基本解分支的周期解和准周期解的非线性动力学分析研究中。事实证明有两种情况是有意义的：轻微、缓慢变化的几何体和轻微、非常缓慢地变化的几何体。对各种情况下的非线性调制方程进行了研究，得到了与以前的线性和数值分析相补充的分析结果。对于微小的、缓慢变化的几何，基本解失去了它的稳定性，而准周期解的存在和稳定性是在非线性调制方程的背景下研究的。在微小的、非常缓慢变化的情况下，存在稳定的空间周期解。
A class of equations is considered which describe the evolution of patterns in problems with a geometry varying slightly, as characterized by a small parameter $ ilde
ull 1 $, and slowly, on a spatial scale $hatepsilon x$ for $hatepsilonll 1$. The model, inspired by the problem of sedimentation in meandering rivers, is generalized for an analytical study of nonlinear dynamics of periodic and quasi-periodic solutions which bifurcate from a basic solution. Two cases prove to be of interest: slightly, slowly varying geometry and slightly, very slowly varying geometry. Nonlinear modulation equations are studied foreach case, yielding analytical results complimentary to previous linear and numerical analyses. For slightly, slowly varying geometry the basic solution loses its stability to quasi-periodic solutions whose existence and stability are studied in the context of the nonlinear modulation equation. In the slightly, very slowly varying case there are stationary spatially periodic solutions of th...