Group foliations, invariant solutions, and conservation laws of the geopotential forecast equation
Abstract
Despite the large number of publications on symmetry analysis of the geopotential forecast equation, its group foliations laws have not been considered previously. The present publication aims to address this shortcoming. First, group foliations are constructed for the equation, and based on them, invariant solutions are derived, some of which generalize previously known exact solutions. There is also a discussion of the pros and cons of the group foliation approach. In addition, the rest of the paper is dedicated to a comprehensive discussion of conservation laws. All possible second-order conservation laws of the geopotential forecast equation are obtained through direct calculations, and a number of higher-order conservation laws are derived using the known symmetries of the equation.
Keywords
Cite
@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}
}
Comments
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