Krein signature and Whitham modulation theory: the sign of characteristics and the “sign characteristic”
Krein signature and Whitham modulation theory: the sign of characteristics and the “sign characteristic”
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Kerin签名和Whitham调制理论：特征的符号和“符号特征”
DOI：
10.1111/sapm.12256
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发表时间：
2019
影响因子：
2.7
通讯作者：
D. Ratliff
中科院分区：
文献类型：
--
作者：
T. Bridges;D. Ratliff
在经典的Whitham调制理论中，无色散的Whitham方程从双曲型到椭圆型的转变与一对非零的纯虚本征值合并并成为复杂的四重态相关联，这表明Krein签名是可操作的。然而，没有自然的辛结构。相反，我们发现操作签名是厄米特矩阵束的真实的特征值的“符号特征”。它在经典的Whitham单相理论中的作用被详细阐述以供说明。然而，符号特性变得重要的主要设置是在多相调制中。结果表明，两个聚结特征成为不稳定（双曲线到椭圆过渡的推广）的必要条件是特征具有相反的符号特征。例如，该理论被应用于耦合非线性薛定谔方程的两相行波解的多相调制。
In classical Whitham modulation theory, the transition of the dispersionless Whitham equations from hyperbolic to elliptic is associated with a pair of nonzero purely imaginary eigenvalues coalescing and becoming a complex quartet, suggesting that a Krein signature is operational. However, there is no natural symplectic structure. Instead, we find that the operational signature is the “sign characteristic” of real eigenvalues of Hermitian matrix pencils. Its role in classical Whitham single‐phase theory is elaborated for illustration. However, the main setting where the sign characteristic becomes important is in multiphase modulation. It is shown that a necessary condition for two coalescing characteristics to become unstable (the generalization of the hyperbolic to elliptic transition) is that the characteristics have opposite sign characteristic. For example the theory is applied to multiphase modulation of the two‐phase traveling wave solutions of coupled nonlinear Schrödinger equation.
对称性、相位调制和非线性波
DOI：
--
发表时间：
2017
期刊：
--
影响因子：
--
作者：
Bridges
通讯作者：
Bridges