Geodesic
Dispersionless integrable systems and the~Bogomolny equations on an~Einstein--Weyl geometry background
Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 1, pp. 41-54

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We obtain a dispersionless integrable system describing a local form of a general three-dimensional Einstein–Weyl geometry with a Euclidean (positive) signature, construct its matrix extension, and show that it leads to the Bogomolny equations for a non-Abelian monopole on an Einstein–Weyl background. We also consider the corresponding dispersionless integrable hierarchy, its matrix extension, and the dressing scheme.
Keywords: dispersionless integrable system, Einstein–Weyl geometry, Yang–Mills–Higgs equations.
Mots-clés : Bogomolny equations 
@article{TMF_2020_205_1_a2,
     author = {L. V. Bogdanov},
     title = {Dispersionless integrable systems and {the~Bogomolny} equations on {an~Einstein--Weyl} geometry background},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2020_205_1_a2/}
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L. V. Bogdanov. Dispersionless integrable systems and the~Bogomolny equations on an~Einstein--Weyl geometry background. Teoretičeskaâ i matematičeskaâ fizika, Tome 205 (2020) no. 1, pp. 41-54. http://geodesic.mathdoc.fr/item/TMF_2020_205_1_a2/