Mock-integrability and stable solitary vortices

TL;DR

This paper investigates long-lived, shape-preserving soliton-like solutions in a non-integrable geophysical fluid model, introducing a new stability indicator called configurational entropy.

Contribution

It demonstrates the existence of stable, soliton-like solutions in the Williams-Yamagata-Flierl equation and proposes configurational entropy as a novel stability measure.

Findings

Existence of long-lived, shape-keeping solutions in the model

Stability during the fusion process of soliton-like objects

Introduction of configurational entropy as a stability indicator

Abstract

Localized soliton-like solutions to a $(2+1)$-dimensional hydro-dynamical evolution equation are studied numerically. The equation is so-called Williams-Yamagata-Flierl equation, which governs geostrophic fluid in a certain parameter range. Although the equation does not have an integrable structure in the ordinary sense, we find there exist shape-keeping solutions with very long life in a special background flow and an initial condition. The stability of the localization at the fusion process of two soliton-like objects is also investigated. As for the indicator of the long-term stability of localization, we propose a concept of configurational entropy, which has been introduced in analysis for non-topological solitons in field theories.