Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background

Abstract

We derive a dispersionless integrable system describing a local form of a general three-dimensional Einstein-Weyl geometry with an Euclidean (positive) signature, construct its matrix extension and demonstrate that it leads to the Bogomolny equations for a non-abelian monopole on an Einstein-Weyl geometry background. The corresponding dispersionless integrable hierarchy, its matrix extension and the dressing scheme are also considered.

15 pages, to be published in Teor. i Mat. Fiz. (a Russian version)

References in corpus (3)

• Integrable Background Geometries
• A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields
• Matrix extension of the Manakov-Santini system and integrable chiral model on Einstein-Weyl background

Cited by in corpus (1)

• Matrix extension of multidimensional dispersionless integrable hierarchies