位势预报方程的分组叶状结构、不变解与守恒律
数学物理
2024-08-16 v3 math.MP
摘要
尽管关于位势预报方程对称性分析的文献众多，其分组叶状结构律此前尚未被考虑。本论文旨在弥补这一不足。首先，为该方程构造分组叶状结构，并基于此导出不变解，其中部分解推广了先前已知的精确解。文中还讨论了分组叶状结构方法的优缺点。此外，论文其余部分致力于对守恒律的全面讨论。通过直接计算得到位势预报方程所有可能的二阶守恒律，并利用该方程的已知对称性导出若干高阶守恒律。
引用
@article{arxiv.2310.14562,
title = {Group foliations, invariant solutions, and conservation laws of the geopotential forecast equation},
author = {E. I. Kaptsov},
journal= {arXiv preprint arXiv:2310.14562},
year = {2024}
}
备注
Since it has recently turned out that the results obtained by the author related to conservation laws are not original, the corresponding part of the text has been revised and provided with a disclaimer