Solitons and the electromagnetic field
type: Item
instance of: scholarly article
title: Solitons and the electromagnetic field
zbMATH Open document ID: 0930.35168
DOI: 10.1007/PL00004759
author: Vieri Benci
author: Donato Fortunato
author: Antonio Masiello
author: Lorenzo Pisani
published in: Mathematische Zeitschrift
publication date: 1999-10-20T00:00:00Z
review text: This paper deals with a model of solitons, in three space dimensions, recently introduced by Benci, Fortunato and Pisani. These solitons are traveling waves with a topological constraint, which is called charge. Since these soliton-like solutions behave as relativistic particles, we introduce a suitable model of interaction between waves and an electromagnetic field. The Lagrangian density of the system is the sum of three terms: the first is that of the free soliton, the second is the classical Lagrangian density of an electromagnetic field, the third is due to the interaction. In particular the last term, which is gauge invariant, is chosen so that the electric charge coincides with the topological charge; moreover, the current density vanishes whenever the charge carried out by the soliton does not move. We prove the existence of a non-trivial static solution (with magnetic field equal to zero). This solution is characterized as a saddle point of the energy functional, which is strongly unbounded from above, as well as from below. In order to deal with a functional which is bounded from below, a suitable variational principle is used. After this reduction, since the domain is unbounded, we use a concentration-compactness argument, which allows to find non-trivial minima.
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 37K40
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 83C50
zbMATH DE Number: 1351166
zbMATH Keywords: traveling waves
zbMATH Keywords: Lagrangian density
zbMATH Keywords: existence
zbMATH Keywords: static solution
zbMATH Keywords: saddle point of the energy functional
zbMATH Keywords: variational principle
zbMATH Keywords: concentration-compactness argument
MaRDI profile type: Publication
full work available at URL: pl00004759
OpenAlex ID: W2027490517
description: scientific article; zbMATH DE number 1351166