Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background
Exactly Solvable and Integrable Systems
2021-06-01 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2005.09906,
title = {Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background},
author = {L. V. Bogdanov},
journal= {arXiv preprint arXiv:2005.09906},
year = {2021}
}
Comments
15 pages, to be published in Teor. i Mat. Fiz. (a Russian version)