Dispersionless integrable systems and the Bogomolny equations on an EinsteinWeyl geometry background
Abstract
We obtain a dispersionless integrable system describing a local form of a general threedimensional EinsteinWeyl geometry with a Euclidean (positive) signature, construct its matrix extension, and show that it leads to the Bogomolny equations for a nonAbelian monopole on an EinsteinWeyl background. We also consider the corresponding dispersionless integrable hierarchy, its matrix extension, and the dressing scheme.
 Publication:

Theoretical and Mathematical Physics
 Pub Date:
 October 2020
 DOI:
 10.1134/S0040577920100037
 arXiv:
 arXiv:2005.09906
 Bibcode:
 2020TMP...205.1279B
 Keywords:

 dispersionless integrable system;
 EinsteinWeyl geometry;
 Bogomolny equations;
 YangMillsHiggs equations;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 37K10;
 37K15;
 37K25;
 35Q75
 EPrint:
 15 pages, to be published in Teor. i Mat. Fiz. (a Russian version)