Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems
Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems
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DOI：
10.1016/j.jde.2006.08.005
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发表时间：
2006-11
影响因子：
2.4
通讯作者：
M. Kuwamura;E. Yanagida
中科院分区：
文献类型：
--
作者：
M. Kuwamura;E. Yanagida
本文研究周期系数线性微分方程组在小扰动下的Hamilton系统。Krein公式决定了单位圆上定乘子的性质，在研究Hamilton系统的（强）稳定性方面有着重要的应用。我们的目的是给出一个简单的公式，确定具有两个重数的不定乘子的行为，这是一般情况。该结果不需要解析性，直接证明。应用这个公式，我们得到了非线性耗散系统如Swift-Hohenberg方程和活化剂-抑制剂型反应扩散系统具有周期结构解的不稳定性准则.
This paper is concerned with Hamiltonian systems of linear differential equations with periodic coefficients under a small perturbation. It is well known that Krein's formula determines the behavior of definite multipliers on the unit circle and is quite useful in studying the (strong) stability of Hamiltonian system. Our aim is to give a simple formula that determines the behavior of indefinite multipliers with two multiplicity, which is generic case. The result does not require analyticity and is proved directly. Applying this formula, we obtain instability criteria for solutions with periodic structure in nonlinear dissipative systems such as the Swift–Hohenberg equation and reaction–diffusion systems of activator–inhibitor type.