Toroidal Soliton Solutions in O(3)^N Nonlinear Sigma Model

TL;DR

This paper explores multi-soliton solutions with arbitrary Hopf numbers in a nonlinear sigma model, demonstrating stability and deriving a generalized inequality, with implications for soliton interactions.

Contribution

It introduces a stable multi-soliton configuration in an O(3)^N model and generalizes the Vakulenko-Kapitansky inequality.

Findings

Multi-soliton static configurations with arbitrary Hopf numbers found

Generalized Vakulenko-Kapitansky inequality derived

Discussion of interaction channels (attractive, repulsive, noninteracting)

Abstract

A set of N three component unit scalar fields in (3+1) Minkowski space-time is investigated. The highly nonlinear coupling between them is chosen to omit the scaling instabilities. The multi-soliton static configurations with arbitrary Hopf numbers are found. Moreover, the generalized version of the Vakulenko-Kapitansky inequality is obtained. The possibility of attractive, repulsing and noninteracting channels is discussed.