About toroidal soliton-particle of extremal space-time film

TL;DR

This paper investigates a nonlinear field model describing a toroidal soliton-particle in extremal space-time, revealing its localized structure, energy convergence, and a novel iterative solution method.

Contribution

It introduces a new model of a toroidal soliton-particle in extremal space-time and proposes an iterative algorithm for its formal power series solution.

Findings

The solution exhibits a deeply embedded time dependence.

Full energy and angular momentum converge at space infinity.

A formal power series iterative method is developed for solutions.

Abstract

Nonlinear field model of extremal space-time film is considered. Its space-localized solution in toroidal coordinates with periodic dependence in time is investigated. A field configuration having a form of the twisted lightlike soliton moving along the ring is considered. An iterative algorithm for obtaining the solution in the form of formal power series in one toroidal variable is proposed. It is discovered that the time dependence in the toroidal solution has a deeply embedded character. Thus the full energy and angular momentum of the solution converge at space infinity.