72 citations · 406 across the 28 of their papers we have counts for
28 papers
A class of reductions of the two-component KP hierarchy and the Hirota-Ohta system
L. V. Bogdanov, Lingling Xue
We introduce a class of reductions of the two-component KP hierarchy, which includes the Hirota-Ohta system hierarchy. The description of the reduced hierarchies is based on the Hi…
Dispersionless BKP equation, the Manakov-Santini system and Einstein-Weyl structures
L. V. Bogdanov
We construct a map of solutions of the dispersionless BKP (dBKP) equation to solutions of the Manakov-Santini (MS) system. This map defines an Einstein-Weyl structure corresponding…
Matrix extension of multidimensional dispersionless integrable hierarchies
L. V. Bogdanov
We consistently develop a recently proposed scheme of matrix extension of dispersionless integrable systems for the general case of multidimensional hierarchies, concentrating on t…
Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background
L. V. Bogdanov
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 mat…
Matrix extension of the Manakov-Santini system and integrable chiral model on Einstein-Weyl background
L. V. Bogdanov
It was demonstrated recently [Dunajski, Ferapontov and Kruglikov (2014)] that the Manakov-Santini system describes a local form of general Lorentzian Einstein-Weyl geometry. We int…
Integrability properties of symmetric 4+4-dimensional heavenly type equation
L. V. Bogdanov, B. G. Konopelchenko
We demonstrate that the dispersionless -dressing method developed before for general heavenly equation is applicable to the and - dimensional symmetric…