Three-dimensional vortex dipole solitons in self-gravitating systems

TL;DR

This paper derives and analyzes three-dimensional vortex dipole solitons in self-gravitating fluids, revealing stable core solutions and unstable superimposed structures, with implications for astrophysical fluid dynamics.

Contribution

It introduces analytical 3D vortex dipole soliton solutions in self-gravitating systems using a novel extension of the Larichev-Reznik method.

Findings

The basic 3D vortex soliton is extremely stable and shape-preserving.

Superimposed monopole or z-antisymmetric parts are unstable but can persist at small amplitudes.

The solutions provide insight into the dynamics of rotating self-gravitating fluids.

Abstract

We derive the nonlinear equations governing the dynamics of three-dimensional (3D) disturbances in a nonuniform rotating self-gravitating fluid under the assumption that the characteristic frequencies of disturbances are small compared to the rotation frequency. Analytical solutions of these equations are found in the form of the 3D vortex dipole solitons. The method for obtaining these solutions is based on the well-known Larichev-Reznik procedure for finding two-dimensional nonlinear dipole vortex solutions in the physics of atmospheres of rotating planets. In addition to the basic 3D x-antisymmetric part (carrier), the solution may also contain radially symmetric (monopole) or/and antisymmetric along the rotation axis (z-axis) parts with arbitrary amplitudes, but these superimposed parts cannot exist without the basic part. The 3D vortex soliton without the superimposed parts is extremely stable. It moves without distortion and retains its shape even in the presence of an initial noise disturbance. The solitons with parts that are radially symmetric or/and z-antisymmetric turn out to be unstable, although at sufficiently small amplitudes of these superimposed parts, the soliton retains its shape for a very long time.