Nested Multi-Soliton Solutions with Arbitrary Hopf Index

TL;DR

This paper constructs and analyzes nested multi-soliton solutions with arbitrary Hopf index in a modified O(3) sigma model, revealing complex toroidal structures and sphaleron-like configurations.

Contribution

It introduces a new class of finite-energy multi-soliton solutions with arbitrary Hopf index, characterized by nested toroidal structures in a generalized sigma model.

Findings

Existence of static multi-soliton configurations with nontrivial Hopf index.

Identification of nested toroidal soliton structures.

Presentation of sphaleron-like solutions with zero topological charge.

Abstract

Generalized Aratyn-Ferreira-Zimerman O(3) nonlinear sigma model with a particular symmetry breaking term, so-called dielectric function, is discussed. Static multi-soliton configurations with finite energy and nontrivial Hopf index are found. We show that such configurations consist of nested toroidal solitons. Moreover, nontrivial sphaleron-like solutions i.e. configurations with zero total topological charge are also presented.