标题： Ginzburg-Landau方程切空间中的严格和挑剔模式分裂 显示英文标题

标题： 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，可以观察到“物理”模式，这些模式在动力学中起重要作用，并且与其余一组双曲“隔离”自由度解耦，这些自由度代表强烈衰减的扰动。 这种模式分裂在不同空间耦合强度下的Ginzburg-Landau方程中进行了研究。 我们观察到，隔离模式与系统均匀稳态的本征模式一致；在局部基下，状态向量的非零分量数目与“物理”模式数目一致；在具有有限自由度的系统中，当耦合达到有限值时，严格的模式分裂消失；在此值以上，观察到模糊的模式分裂。 显示英文摘要

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.