标题： 海洋非线性内波的群分析。 I：自伴性，守恒定律，不变解 显示英文标题

标题： Group Analysis of Nonlinear Internal Waves in Oceans. I: Self-adjointness, conservation laws, invariant solutions

摘要： 本文致力于研究在地球物理流体动力学中作为基本模型的二维均匀分层旋转流体运动方程的群分析。 结果显示，所讨论的非线性方程具有一个显著的性质，即自伴随性。 这一性质对于本文中提出的守恒定律的构建至关重要。 利用某些对称性构造了不变解。 不变解用于定义内部波束。 显示英文摘要

摘要： The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.