Generalized Eikonal Knots and New Integrable Dynamical Systems

TL;DR

This paper introduces a new class of non-linear O(3) models that yield integrable submodels with exact solutions for toroidal solitons and knots, expanding the understanding of topological solitons in mathematical physics.

Contribution

It presents a novel class of non-linear models with integrability conditions, providing explicit solutions for toroidal and knotted topological solitons.

Findings

Exact solutions for toroidal solitons with non-trivial Hopf index.

Analysis of the generalized eikonal equation.

Construction of topological solutions describing torus knots and multi-knot configurations.

Abstract

A new class of non-linear O(3) models is introduced. It is shown that these systems lead to integrable submodels if an additional integrability condition (so called the generalized eikonal equation) is imposed. In the case of particular members of the family of the models the exact solutions describing toroidal solitons with a non-trivial value of the Hopf index are obtained. Moreover, the generalized eikonal equation is analyzed in detail. Topological solutions describing torus knots are presented. Multi-knot configurations are found as well.