Cauchy matrix approach to the SU(2) self‐dual Yang–Mills equation
Shangshuai Li, Changzheng Qu, Xiangxuan Yi, Da‐jun Zhang
Abstract
Abstract The Cauchy matrix approach is developed to solve the self‐dual Yang–Mills (SDYM) equation. Starting from a Sylvester matrix equation coupled with certain dispersion relations for an infinite number of coordinates, we derive some new relations that give rise to the SDYM equation under Yang's formulation. By imposing further constraints on complex independent variables, a broad class of explicit solutions of the equation under Yang's formulation are obtained.
Topics & Concepts
MathematicsCauchy matrixMatrix (chemical analysis)Matrix differential equationSylvester equationMatrix difference equationCauchy distributionDual (grammatical number)Class (philosophy)Mathematical analysisMathematical physicsPure mathematicsRiccati equationApplied mathematicsDifferential equationCauchy boundary conditionPhysicsEigenvalues and eigenvectorsBoundary value problemQuantum mechanicsLiteratureArtMaterials scienceArtificial intelligenceComputer scienceComposite materialFree boundary problemNonlinear Waves and SolitonsAlgebraic structures and combinatorial modelsNonlinear Photonic Systems