SDYM equations on the self-dual background

Abstract

We introduce the technique combining the features of integration schemes for SDYM equations and multidimensional dispersionless integrable equations to get SDYM equations on the conformally self-dual background. Generating differential form is defined, the dressing scheme is developed. Some special cases and reductions are considered.

arXiv commentBased on the talk presented at LMS -- EPSRC Durham Symposium "Geometric and Algebraic Aspects of Integrability", 25 July - 4 August 2016

References in corpus (7)

• The Cauchy Problem on the Plane for the Dispersionless Kadomtsev - Petviashvili Equation
• Anti-self-dual four-manifolds with a parallel real spinor
• Dunajski generalization of the second heavenly equation: dressing method and the hierarchy
• On the Einstein-Weyl and conformal self-duality equations
• Integrable Background Geometries
• On a class of multidimensional integrable hierarchies and their reductions
• Volume-preserving diffeomorphisms in integrable deformations of selfdual gravity

Cited by in corpus (3)

• Matrix extension of the Manakov-Santini system and integrable chiral model on Einstein-Weyl background
• Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background
• Matrix extension of multidimensional dispersionless integrable hierarchies