A generalized sideband stability theory via center manifold projection
A generalized sideband stability theory via center manifold projection
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基于中心流形投影的广义边带稳定性理论
DOI：
10.1063/1.857586
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
Hsueh
中科院分区：
文献类型：
--
作者：
M. Cheng;Hsueh
中心流形理论用于确定对有限振幅单色波的首阶边带稳定性有显著贡献的所有模式。基于Ginzburg-Landau方程的经典多尺度理论被扩展到远离近临界条件，并被证明忽略了低波数模式的非线性相互作用的重要贡献。稳定的单色波的稳定性界限的色散系统，扩展了经典的Eckhaus界的非色散系统和Lange-Newell和Benjamin-Feir稳定性条件的单色波与临界波数。通过计算模型方程的演化谱，数值验证了这些新的稳定界。
A center manifold theory is used to determine all modes that contribute significantly to the leading‐order sideband stability of finite‐amplitude monochromatic waves. The classical multiscale theories based on the Ginzburg–Landau equation are extended away from near‐critical conditions and are shown to have omitted an important contribution from nonlinear interactions with low wave‐number modes. Stability bounds on stable monochromatic waves are reported for dispersive systems that extend the classical Eckhaus bound for nondispersive systems and the Lange–Newell and Benjamin–Feir stability conditions for monochromatic waves with critical wave numbers. These new stability bounds are verified numerically by computing the evolving spectrum of a model equation.