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pro vyhledávání: '"Adler, V. E."'
Autor:
Adler, V. E.
We study the 3D-consistency property for negative symmetries of KdV type equations. Its connection with the 3D-consistency of discrete equations is explained.
Comment: 19 pages
Comment: 19 pages
Externí odkaz:
http://arxiv.org/abs/2407.09813
Autor:
Adler, V. E.
A construction of negative flows for integrable systems based on the Lax representation and squared eigenfunctions is proposed. Examples considered include the Boussinesq equation and its reduction to the Sawada-Kotera and Kaup-Kupershmidt equations;
Externí odkaz:
http://arxiv.org/abs/2310.11549
Autor:
Adler, V. E.
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Special Issue in Memory of Decio Levi (February 15, 2024) ocnmp:11597
We study reductions of the Volterra lattice corresponding to stationary equations for the additional, noncommutative subalgebra of symmetries. It is shown that, in the case of general position, such a reduction is equivalent to the stationary equatio
Externí odkaz:
http://arxiv.org/abs/2307.08127
Autor:
Adler, V. E., Kolesnikov, M. P.
Publikováno v:
J. Math. Phys. 64, 101505 (2023)
We study reductions of the Korteweg--de Vries equation corresponding to stationary equations for symmetries from the noncommutative subalgebra. An equivalent system of $n$ second-order equations is obtained, which reduces to the Painlev\'e equation P
Externí odkaz:
http://arxiv.org/abs/2304.11590
Autor:
Adler, V. E., Kolesnikov, M. P.
Publikováno v:
J. Math. Phys. 2022; 63 (10): 103504
In integrable models, stationary equations for higher symmetries serve as one of the main sources of reductions consistent with dynamics. We apply this method to the non-Abelian two-dimensional Toda lattice. It is shown that already the stationary eq
Externí odkaz:
http://arxiv.org/abs/2203.09977
Autor:
Adler, V. E.
We study the problem of the decay of initial data in the form of a unit step for the Bogoyavlensky lattices. In contrast to the Gurevich--Pitaevskii problem of the decay of initial discontinuity for the KdV equation, it turns out to be exactly solvab
Externí odkaz:
http://arxiv.org/abs/2202.02555
Autor:
Adler, V. E.
Publikováno v:
Ufa Math. J. 13:2 (2021) 107-114
We construct non-Abelian analogs for some KdV type equations, including the (rational form of) exponential Calogero--Degasperis equation and generalizations of the Schwarzian KdV equation. Equations and differential substitutions under study contain
Externí odkaz:
http://arxiv.org/abs/2103.04370
Autor:
Adler, V. E., Sokolov, V. V.
Publikováno v:
Theoret. Math. Phys. 207:2 (2021) 560-571
The Painlev\'e--Kovalevskaya test is applied to find three matrix versions of the Painlev\'e II equation. All these equations are interpreted as group-invariant reductions of integrable matrix evolution equations, which makes it possible to construct
Externí odkaz:
http://arxiv.org/abs/2012.05639
Autor:
Adler, V. E.
Publikováno v:
2021 J. Phys. A: Math. Theor. 54 035204
The Volterra lattice admits two non-Abelian analogs that preserve the integrability property. For each of them, the stationary equation for non-autonomous symmetries defines a constraint that is consistent with the lattice and leads to Painlev\'e-typ
Externí odkaz:
http://arxiv.org/abs/2010.09021
Autor:
Adler, V. E., Sokolov, V. V.
Publikováno v:
Math. Phys. Anal. Geom. 24:1 (2021) 7
We find noncommutative analogs for well-known polynomial evolution systems with higher conservation laws and symmetries. The integrability of obtained non-Abelian systems is justified by explicit zero curvature representations with spectral parameter
Externí odkaz:
http://arxiv.org/abs/2008.09174