Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.
Wave-packet formation at the zero-dispersion point in the Gardner-Ostrovsky equation.
复制标题
加德纳-奥斯特洛夫斯基方程中零色散点的波包形成。
DOI：
10.1103/physreve.91.051201
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
Edward R. Johnson
中科院分区：
文献类型：
--
作者：
A. Whitfield;Edward R. Johnson
弱旋转对内部孤立波的长期影响是衰减成惯性重力波，并最终出现相干、稳定传播的非线性波包。目前对于这些波包形成的原因还没有完全令人满意的解释。这里，初始值问题是在 Gardner-Ostrovsky 方程或旋转修正扩展 Korteweg-de Vries 方程的背景下考虑的。线性加德纳-奥斯特洛夫斯基方程在临界波数（通常称为零色散点）处具有最大群速度。这里发现，波数谱在零色散点处的非线性分裂，即能量转移到加德纳-奥斯特洛夫斯基方程的调制不稳定区域，是波包形成的原因。加德纳-奥斯特洛夫斯基方程中孤立波的衰减与零色散点处的非线性薛定谔方程的数值比较可用于确认光谱分裂。
The long-time effect of weak rotation on an internal solitary wave is the decay into inertia-gravity waves and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. There is currently no entirely satisfactory explanation as to why these wave packets form. Here the initial value problem is considered within the context of the Gardner-Ostrovsky, or rotation-modified extended Korteweg-de Vries, equation. The linear Gardner-Ostrovsky equation has maximum group velocity at a critical wave number, often called the zero-dispersion point. It is found here that a nonlinear splitting of the wave-number spectrum at the zero-dispersion point, where energy is shifted into the modulationally unstable regime of the Gardner-Ostrovsky equation, is responsible for the wave-packet formation. Numerical comparisons of the decay of a solitary wave in the Gardner-Ostrovsky equation and a derived nonlinear Schrödinger equation at the zero-dispersion point are used to confirm the spectral splitting.