The reduced self-dual Yang–Mills equation, binary and infinitesimal Darboux transformations

DOI10.1063/1.532346zbMath0921.58009OpenAlexW2038994441MaRDI QIDQ4213010

Nikolai V. Ustinov

Publication date: 9 May 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532346

zbMATH Keywords

Darboux transformationsselfdual Yang-Mills equations\((2+1)\)-dimensional spacetimes

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

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Cites Work

• The reduction problem and the inverse scattering method
• Representation theory and integration of nonlinear spherically symmetric equations to gauge theories
• A self-dual Yang-Mills hierarchy and its reductions to integrable systems in \(1+1\) and \(2+1\) dimensions
• Additional symmetries for integrable equations and conformal algebra representation
• Scattering data for the self-duality equations
• Conserved quantities and symmetries of KP hierarchy
• Integrable and solvable systems, and relations among them
• Third order spectral problems: reductions and Darboux transformations
• SQUARED EIGENFUNCTIONS OF THE (MODIFIED) KP HIERARCHY AND SCATTERING PROBLEMS OF LOEWNER TYPE