Solitary Waves and Electromagnetic Fields

Donato Fortunato

Bollettino dell'Unione Matematica Italiana (2008)

  • Volume: 1, Issue: 3, page 767-789
  • ISSN: 0392-4041

Abstract

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Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet; by soliton, we mean a solitary wave which exhibits some form of stability. In this respect solitary waves and solitons have a particle-like behavior and they occur in many questions of mathematical physics, such as superconductivity, phase transition, classical and quantum field theory, non linear optics, (see e.g. [37], [50], [56]). We are not interested in the study of a particular model. Here we shall be concerned with the existence of solitary waves for a class of variational field equations which exhibit suitable symmetry properties, namely equations which are invariant for the Poincarè group and the gauge group. In particular we shall describe two results obtained jointly with V. Benci in [17], [18]. These results state the existence of three dimensional vortices for Abelian gauge theories describing the interaction of electrically charged solitary waves with the electromagnetic field.

How to cite

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Fortunato, Donato. "Solitary Waves and Electromagnetic Fields." Bollettino dell'Unione Matematica Italiana 1.3 (2008): 767-789. <http://eudml.org/doc/290470>.

@article{Fortunato2008,
abstract = {Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet; by soliton, we mean a solitary wave which exhibits some form of stability. In this respect solitary waves and solitons have a particle-like behavior and they occur in many questions of mathematical physics, such as superconductivity, phase transition, classical and quantum field theory, non linear optics, (see e.g. [37], [50], [56]). We are not interested in the study of a particular model. Here we shall be concerned with the existence of solitary waves for a class of variational field equations which exhibit suitable symmetry properties, namely equations which are invariant for the Poincarè group and the gauge group. In particular we shall describe two results obtained jointly with V. Benci in [17], [18]. These results state the existence of three dimensional vortices for Abelian gauge theories describing the interaction of electrically charged solitary waves with the electromagnetic field.},
author = {Fortunato, Donato},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {767-789},
publisher = {Unione Matematica Italiana},
title = {Solitary Waves and Electromagnetic Fields},
url = {http://eudml.org/doc/290470},
volume = {1},
year = {2008},
}

TY - JOUR
AU - Fortunato, Donato
TI - Solitary Waves and Electromagnetic Fields
JO - Bollettino dell'Unione Matematica Italiana
DA - 2008/10//
PB - Unione Matematica Italiana
VL - 1
IS - 3
SP - 767
EP - 789
AB - Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet; by soliton, we mean a solitary wave which exhibits some form of stability. In this respect solitary waves and solitons have a particle-like behavior and they occur in many questions of mathematical physics, such as superconductivity, phase transition, classical and quantum field theory, non linear optics, (see e.g. [37], [50], [56]). We are not interested in the study of a particular model. Here we shall be concerned with the existence of solitary waves for a class of variational field equations which exhibit suitable symmetry properties, namely equations which are invariant for the Poincarè group and the gauge group. In particular we shall describe two results obtained jointly with V. Benci in [17], [18]. These results state the existence of three dimensional vortices for Abelian gauge theories describing the interaction of electrically charged solitary waves with the electromagnetic field.
LA - eng
UR - http://eudml.org/doc/290470
ER -

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