Ginzburg-Landau方程切空间中的严格模分裂和模糊模分裂
Strict and fussy mode splitting in the tangent space of the Ginzburg-Landau equation
摘要：
在某些空间扩展耗散系统的切空间中，人们可以观察到高度参与动力学的“物理”模式，并且与代表强烈衰减扰动的剩余双曲“隔离”自由度组解耦。研究了不同空间耦合强度下的Ginzburg-Landau方程的模式分裂。我们观察到，孤立的模式与系统的均匀稳定状态的本征模式相一致;有一个本地的基础上，状态向量的非零分量的数量与“物理”模式的数量相一致;在一个系统中，有限数量的自由度的严格模式分裂消失在有限的耦合值;在此值以上的一个模糊的模式分裂观察。
英文摘要：
In the tangent space of some spatially extended dissipative systems one can observe "physical" modes which are highly involved in the dynamics and are decoupled from the remaining set of hyperbolically "isolated" degrees of freedom representing strongly decaying perturbations. This mode splitting is studied for the Ginzburg-Landau equation at different strength of the spatial coupling. We observe that isolated modes coincide with eigenmodes of the homogeneous steady state of the system; that there is a local basis where the number of non-zero components of the state vector coincides with the number of "physical" modes; that in a system with finite number of degrees of freedom the strict mode splitting disappears at finite value of coupling; that above this value a fussy mode splitting is observed.
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