On the connection between harmonic maps and the self-dual Yang-Mills and the sine-Gordon equations

DOI10.1016/0393-0440(92)90053-4zbMath0747.58025OpenAlexW2089317367WikidataQ62125791 ScholiaQ62125791MaRDI QIDQ1184390

Karen K. Uhlenbeck

Publication date: 28 June 1992

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(92)90053-4

zbMATH Keywords

harmonic mapssine-Gordon equationself-dual Yang-Mills equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Yang-Mills and other gauge theories in quantum field theory (81T13) Harmonic maps, etc. (58E20) Abstract harmonic analysis (43A99)

Related Items

Simple factor dressing and the López-Ros deformation of minimal surfaces in Euclidean 3-space, Generalized self-dual Yang-Mills flows, explicit solutions and reductions, Integrable evolution systems based on generalized self-dual Yang-Mills equations and their soliton-like solutions, Two-dimensional integrable systems and self-dual Yang–Mills equations, Harmonic maps from super Riemann surfaces, The symmetries of solitons, Elliptic Integrable Systems: a Comprehensive Geometric Interpretation, Applications of quaternionic holomorphic geometry to minimal surfaces, BÄCKLUND TRANSFORMATIONS AND LAX PAIRS FOR THE NONLINEAR KLEIN–GORDON EQUATION WITH SYMBOLIC COMPUTATION, Vortex string dynamics in an external antisymmetric tensor field, Bäcklund theorems in three-dimensional de Sitter space and anti-de Sitter space

Cites Work

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• Classical solutions of two-dimensional Grassmannian models
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• On the energy spectrum of harmonic 2-spheres in unitary groups
• Integrable Hamiltonian systems and interactions through quadratic constraints
• Minimal immersions of surfaces in Euclidean spheres
• The Self-Duality Equations on a Riemann Surface