Applications of Darboux transformations to the self-dual Yang-Mills equations

DOI10.1007/BF02551200zbMath0971.53022MaRDI QIDQ1586706

Yasuhiro Ohta, Jonathan J. C. Nimmo, Claire R. Gilson

Publication date: 23 November 2000

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

exact solutionself-dual Yang-Mills equationsDarboux transformationLax pair

Mathematics Subject Classification ID

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Related Items (16)

Binary Darboux transformation of time-discrete generalized lattice Heisenberg magnet model ⋮ Reductions of Darboux transformations for the \(\mathcal{PT}\)-symmetric nonlocal Davey-Stewartson equations ⋮ Darboux transformation and soliton solutions of the spatial discrete coupled complex short pulse equation ⋮ New soliton solutions of anti-self-dual Yang-Mills equations ⋮ Binary Darboux transformation for the Gerdjikov-Ivanov equation ⋮ Darboux Transformation for the Hirota Equation ⋮ Darboux transformation and soliton solutions for a nonlocal two-component complex modified Korteweg-de Vries equation ⋮ Solutions to the \(\mathrm{SU}(\mathcal{N})\) self-dual Yang-Mills equation ⋮ Dynamics of rogue waves in the partially \(\mathcal{PT}\)-symmetric nonlocal Davey-Stewartson systems ⋮ Soliton scattering in noncommutative spaces ⋮ Solitons and dynamics for a general integrable nonlocal coupled nonlinear Schrödinger equation ⋮ Binary Darboux transformations of the supersymmetric Heisenberg magnet model ⋮ On Darboux transformations for the derivative nonlinear Schrödinger equation ⋮ Exact solutions of the Gerdjikov-Ivanov equation using Darboux transformations ⋮ Quasi-Grammian solutions of a multi-component short pulse equation ⋮ Multi-soliton dynamics of anti-self-dual gauge fields

Cites Work

• Self-dual Yang-Mills fields over a sphere
• Darboux transformation and explicit solutions of the Kadomtsev-Petviashvili equation, depending on functional parameters
• Instantons and algebraic geometry
• The reduced self-dual Yang–Mills equation, binary and infinitesimal Darboux transformations
• Bilinear Form Approach to the Self-Dual Yang-Mills Equations and Integrable Systems in (2+1)-Dimension

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