A dispersionless integrable system associated to Diff$(S^1)$ gauge theory

Abstract

A dispersionless integrable system underlying 2+1-dimensional hyperCR Einstein--Weyl structures is obtained as a symmetry reduction of the anti--self--dual Yang--Mills equations with the gauge group Diff$(S^1)$. Two special classes of solutions are obtained from well known soliton equations by embedding SU(1,1) in $Diff(S^1)$.

Final version, to appear in Physics Letters A

References in corpus (2)

• Hydrodynamic reductions and solutions of a universal hierarchy
• Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type

Cited by in corpus (4)

• Integrable Background Geometries
• On Reductions of Noncommutative Anti-Self-Dual Yang-Mills Equations
• Linearly degenerate hierarchies of quasiclassical SDYM type
• Multidimensional integrable systems and deformations of Lie algebra homomorphisms