Group Analysis of Nonlinear Internal Waves in Oceans. II: The symmetries and rotationally invariant solution

TL;DR

This paper identifies the maximal Lie symmetry group of nonlinear oceanic internal wave equations, constructs rotationally invariant solutions, and analyzes their qualitative behavior and energy properties.

Contribution

It determines the infinite-dimensional symmetry group of the equations and derives invariant solutions, advancing understanding of symmetries in geophysical fluid dynamics.

Findings

Infinite-dimensional Lie symmetry group involving three arbitrary functions of time

Construction of rotationally invariant solutions

Qualitative analysis and energy calculation of solutions

Abstract

74J30The maximal group of Lie point symmetries of a system of nonlinear equations used in geophysical fluid dynamics is presented. The Lie algebra of this group is infinite-dimensional and involves three arbitrary functions of time. The invariant solution under the rotation and dilation is constructed. Qualitative analysis of the invariant solution is provided and the energy of this solution is presented.