Zobrazeno 1 - 10
of 277
pro vyhledávání: '"Bogdanov L"'
Autor:
Bogdanov, L. V.
We use a recently proposed scheme of matrix extension of dispersionless integrable systems for the Abelian case, in which it leads to linear equations, connected with the initial dispersionless system. In the examples considered, these equations can
Externí odkaz:
http://arxiv.org/abs/2404.18078
Autor:
Bogdanov, L. V., Xue, Lingling
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 Hirota bilinear identity and an extra bilinear relation characterising t
Externí odkaz:
http://arxiv.org/abs/2112.12759
Autor:
Bogdanov, L. V.
Publikováno v:
Symmetry 2021, 13(9), 1699
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 to the dBKP equation through the general Lorentzian Einstein-Weyl str
Externí odkaz:
http://arxiv.org/abs/2108.03078
Autor:
Bogdanov, L. V.
We consistently develop a recently proposed scheme of matrix extension of dispersionless integrable systems for the general case of multidimensional hierarchies, concentrating on the case of dimension $d\geqslant 4$. We present extended Lax pairs, La
Externí odkaz:
http://arxiv.org/abs/2105.14264
Autor:
Bogdanov, L. V.
Publikováno v:
Theoretical and Mathematical Physics 205, 1279-1290 (2020)
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
Externí odkaz:
http://arxiv.org/abs/2005.09906
Autor:
Bogdanov, L. V.
Publikováno v:
Theoretical and Mathematical Physics 201(3):1701-1709 (2019)
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 introduce integrable matrix extension of the Manakov-Santini system and s
Externí odkaz:
http://arxiv.org/abs/1907.01964
Autor:
Bogdanov, L. V., Konopelchenko, B. G.
We demonstrate that the dispersionless $\bar\partial$-dressing method developed before for general heavenly equation is applicable to the $4+4$ and $2N+2N$ - dimensional symmetric heavenly type equations. We introduce generating relation and derive t
Externí odkaz:
http://arxiv.org/abs/1905.00887
Autor:
Bogdanov, L. V., Pavlov, M. V.
We consider six-dimensional heavenly equation as a reduction in the framework of general six-dimensional linearly degenerate dispersionless hierarchy. We characterise the reduction in terms of wave functions, introduce generating relation, Lax-Sato e
Externí odkaz:
http://arxiv.org/abs/1806.01500
Autor:
Bogdanov, L. V.
We introduce the technique combining the features of integration schemes for SDYM equations and multidimensional dispersionless integrable equations to get SDYM equations on the conformally self-dual background. Generating differential form is define
Externí odkaz:
http://arxiv.org/abs/1612.04536
Autor:
Bogdanov, L. V., Pavlov, M. V.
We demonstrate that SDYM equations for the Lie algebra of one-dimensional vector fields represent a natural reduction in the framework of general linearly degenerate dispersionless hierarchy. We define the reduction in terms of wave functions, introd
Externí odkaz:
http://arxiv.org/abs/1603.00238