Domain Wall Solitons Arising in Classical Gauge Field Theories

Lei Cao, Shouxin Chen, Yisong Yang

Research output: Contribution to journalArticle

Abstract

Domain wall solitons are basic constructs realizing phase transitions in various field-theoretical models and are solutions to some nonlinear ordinary differential equations descending from the corresponding full sets of governing equations in higher dimensions. In this paper, we present a series of domain wall solitons arising in several classical gauge field theory models. In the context of the Abelian gauge field theory, we unveil the surprising result that the solutions may explicitly be constructed, which enriches our knowledge on integrability of the planar Liouville type equations in their one-dimensional limits. In the context of the non-Abelian gauge field theory, we obtain some existence theorems for domain wall solutions arising in the electroweak type theories by developing some methods of calculus of variations formulated as direct and constrained minimization problems over a weighted Sobolev space.

Original languageEnglish (US)
JournalCommunications In Mathematical Physics
DOIs
StatePublished - Jan 1 2019

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Classical Field Theory
Gauge Field Theories
Domain Wall
domain wall
Solitons
solitary waves
Sobolev space
existence theorems
calculus of variations
Constrained Minimization
Weighted Sobolev Spaces
Type Theory
Calculus of variations
Nonlinear Ordinary Differential Equations
Minimization Problem
Theoretical Model
Existence Theorem
Integrability
Higher Dimensions
Governing equation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Domain Wall Solitons Arising in Classical Gauge Field Theories. / Cao, Lei; Chen, Shouxin; Yang, Yisong.

In: Communications In Mathematical Physics, 01.01.2019.

Research output: Contribution to journalArticle

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