Solitons in several space dimensions: Derrick's problem and infinitely many solutions
type: Item
instance of: scholarly article
title: Solitons in several space dimensions: Derrick's problem and infinitely many solutions
zbMATH Open document ID: 0973.35161
published in: Archive for Rational Mechanics and Analysis
publication date: 2001-12-10T00:00:00Z
review text: From authors' summary: We study a class of Lorentz invariant nonlinear field equations is several space dimensions. The main purpose is to obtain soliton-like solutions. These equations were essentially proposed by C. H. Derrick in a celebrated paper in 1964 as a model for elementary particles. However, an existence theory was not developed. The fields are characterized by a topological invariant, the charge. We prove the existence of a static solution which minimizes the energy among the configuration with nontrivial charge. Moreover, under some symmetry assumptions, we prove the existence of infinitely many solutions, which are constrained minima of the energy. More precisely, for every \(n\in\mathbb{N}\) there exists a solution of charge \(n\).
Mathematics Subject Classification ID: 35Q51
Mathematics Subject Classification ID: 37K40
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 1538593
zbMATH Keywords: Lorentz invariant nonlinear field equations
zbMATH Keywords: soliton-like solutions
zbMATH Keywords: model for elementary particles
zbMATH Keywords: charge
author: Vieri Benci
author: Pietro d'Avenia
author: Donato Fortunato
author: Lorenzo Pisani
reviewed by: Anthony D. Osborne
MaRDI profile type: Publication
full work available at URL: s002050000101
OpenAlex ID: W2106260664
DOI: 10.1007/S002050000101
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description: scientific article; zbMATH DE number 1538593