Modulational Instability and Variational Structure
Modulational Instability and Variational Structure
复制标题
调制不稳定性和变分结构
DOI：
10.1111/sapm.12029
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发表时间：
2013
影响因子：
2.7
通讯作者：
V. M. Hur
中科院分区：
文献类型：
--
作者：
J. Bronski;V. M. Hur
研究了一维哈密顿系统周期行波的调制不稳定性。我们研究了相关线性化算子的Jordan块结构如何在Floquet指数的小值下分岔，以导出根据动能和势能、动量、底层波的质量及其导数来控制长波扰动的不稳定性的判据。方程的色散算子允许是非局部的，对于这种情况，Evans函数技术可能不适用。我们通过讨论Korteweg‐de Vries型的解析方程和数值方程来说明结果。
We study the modulational instability of periodic traveling waves for a class of Hamiltonian systems in one spatial dimension. We examine how the Jordan block structure of the associated linearized operator bifurcates for small values of the Floquet exponent to derive a criterion governing instability to long wavelengths perturbations in terms of the kinetic and potential energies, the momentum, the mass of the underlying wave, and their derivatives. The dispersion operator of the equation is allowed to be nonlocal, for which Evans function techniques may not be applicable. We illustrate the results by discussing analytically and numerically equations of Korteweg‐de Vries type.