Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems

Multi-Pulse Evolution and Space-Time Chaos in Dissipative Systems
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耗散系统中的多脉冲演化和时空混沌

DOI：
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发表时间：
2009
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影响因子：
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通讯作者：
A. Mielke
A. Mielke
中科院分区：
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文献类型：
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作者：
S. Zelik;A. Mielke

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研究了全空间Rn上的半线性抛物方程组， 通过平移获得的指数衰减脉冲状稳态的家庭。 所考虑的多脉冲解看起来像是无穷多个 这种脉冲被很好地分离。我们证明了一个全局中心流形约化 定理的时间演变，这样的多脉冲解决方案，并表明， 这些解的动力学可以用一个无穷常微分方程系统来描述， 脉冲的位置。 作为所发展理论的一个应用，我们证明了Sinai-Bunimovich的存在性 一维时空周期强迫Swift-Hohenberg时空混沌 方程
We study semilinear parabolic systems on the full space Rn that admit a family of exponentially decaying pulse-like steady states obtained via translations. The multi-pulse solutions under consideration look like the sum of infinitely many such pulses which are well separated. We prove a global center-manifold reduction theorem for the temporal evolution of such multi-pulse solutions and show that the dynamics of these solutions can be described by an infinite system of ODEs for the positions of the pulses. As an application of the developed theory, we verify the existence of SinaiBunimovich space-time chaos in 1D space-time periodically forced Swift-Hohenberg equation.