发表机构
Tomsk Polytechnic University; Tomsk State University of Control Systems and Radioelectronics（托木斯克理工大学; 托木斯克国立控制论和无线电电子大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
受规范场描述启发，本文为常位势涡度浅水方程构建简单拉格朗日量，不依赖辅助场，并利用群论方法找到与标度对称性相关的新精确解。
AI 中文摘要
受近期浅水方程规范场描述的启发 [SciPost Phys. 14 (2023) 102]，本文针对常位势涡度情形构建了一个简单的拉格朗日量表述。该构造的一个吸引人之处在于，它不依赖于类似 Clebsch 的参数化或辅助场的引入。文中还强调，在赤道处，当科里奥利参数为零时，浅水方程表现出额外的 SO(2,1) 共形不变性。利用群论方法，找到了一个新的精确解，该解与共形群中的标度对称性变换相关。
英文摘要
Inspired by a recent gauge field description of shallow water equations [SciPost Phys. 14 (2023) 102], in this work we build a simple Lagrangian formulation for the case of constant potential vorticity. An attractive feature of the construction is that it does not appeal to a Clebsch-like parametrization or the use of auxiliary fields. It is also emphasized that on the equator, where the Coriolis parameter vanishes, the shallow water equations exhibit extra SO(2,1) conformal invariance. Using the group-theoretic method, a new exact solution is found, which is associated with the scaling symmetry transformation entering the conformal group.
Comments15 pages
