Geometric solitons with vortex structures for some geometric flows from Minkowski spaces: part I

TL;DR

This paper constructs geometric solitons with vortex structures for certain geometric flows from Minkowski spaces to the sphere, using a perturbation approach to analyze wave maps and Schrödinger flows.

Contribution

It introduces a perturbation method to explicitly construct vortex-structured solitons for geometric flows from Minkowski spaces, expanding understanding of vortex solutions in this context.

Findings

Constructed vortex pair and vortex ring solitons

Applied perturbation approach to wave maps and Schrödinger flows

Enhanced understanding of vortex structures in Minkowski space flows

Abstract

By a perturbation approach, we construct geometric solitons with various vortex structures(vortex pairs, vortex rings) for some geometric flows(Wave maps, Shr\"odinger flows) from Minkowski spaces to ${\mathbb S}^2\subset\R^3$.