Department of Applied Mathematics, State University of Colorado, Boulder, Colorado 80303, USA.
Department of Mathematics, State University of New York, Buffalo, New York 14260, USA.
Phys Rev E. 2017 Sep;96(3-1):032225. doi: 10.1103/PhysRevE.96.032225. Epub 2017 Sep 25.
Whitham modulation theory for the two-dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasilinear first-order partial differential equations is derived. The system describes modulations of the traveling wave solutions of the 2DBO equation. These equations are transformed to a singularity-free hydrodynamic-like system referred to here as the 2DBO-Whitham system. Exact reductions of this system are discussed, the formulation of initial value problems is considered, and the system is used to study the transverse stability of traveling wave solutions of the 2DBO equation.
本文介绍了二维 Benjamin-Ono（2DBO）方程的 Whitham 调制理论。推导了一个五阶拟线性一阶偏微分方程组。该系统描述了 2DBO 方程行波解的调制。这些方程被转化为一个无奇点的类流体力学系统，这里称为 2DBO-Whitham 系统。讨论了该系统的精确约化，考虑了初值问题的提法，并将该系统用于研究 2DBO 方程行波解的横向稳定性。
