Zobrazeno 1 - 10
of 368
pro vyhledávání: '"Aratyn, H."'
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Proceedings: OCNMP Conference, Bad Ems (Germany), 23-29 June 2024 (April 15, 2024) ocnmp:13201
We present a construction of a class of rational solutions of the Painlev\'e V equation that exhibit a two-fold degeneracy, meaning that there exist two distinct solutions that share identical parameters. The fundamental object of our study is the or
Externí odkaz:
http://arxiv.org/abs/2310.01585
Under special conditions the Painlev\'e V equation has more than one rational solution solving it with the same parameters. In the setting of formalism that identifies points on orbits of the fundamental shift operators of $A^{(1)}_{3}$ affine Weyl g
Externí odkaz:
http://arxiv.org/abs/2307.07825
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Volume 3 (September 6, 2023) ocnmp:11714
We show how the zero-curvature equations based on a loop algebra of $D_4$ with a principal gradation reduce via self-similarity limit to a polynomial Hamiltonian system of coupled Painlev\'e III models with four canonical variables and $D_4^{(1)}$ af
Externí odkaz:
http://arxiv.org/abs/2304.10035
We develop a systematic approach to deriving rational solutions and obtaining classification of their parameters for dressing chains of even N periodicity or equivalently $A^{(1)}_{N-1}$ invariant Painlev\'e equations. This construction identifies ra
Externí odkaz:
http://arxiv.org/abs/2206.06482
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Volume 2 (November 10, 2022) ocnmp:10161
We propose a Hamiltonian formalism for $N$ periodic dressing chain with the even number $N$. The formalism is based on Dirac reduction applied to the $N+1$ periodic dressing chain with the odd number $N+1$ for which the Hamiltonian formalism is well
Externí odkaz:
http://arxiv.org/abs/2109.03869
Publikováno v:
J. Phys. A54 2021, 195701
We identify the self-similarity limit of the second flow of $sl(N)$ mKdV hierarchy with the periodic dressing chain thus establishing % a connection to $A^{(1)}_{N-1}$ invariant Painlev\'e equations. The $A^{(1)}_{N-1}$ B\"acklund symmetries of dress
Externí odkaz:
http://arxiv.org/abs/2101.05859
We extend Painlev\'e IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlev\'e IV and II equations for special limits of the underlying parameters. We deriv
Externí odkaz:
http://arxiv.org/abs/2009.05219
Publikováno v:
J. Phys.: Conf. Ser. 1194, (2019) 012002
We discuss symmetries of Hamiltonians of I$_{38}$ and I$_{49}$ equations that appear on Ince's list of fifty second-order differential equations with Painlev\'e property. This study is informed by structure of Weyl symmetries of Painlev\'e P$_{III}$
Externí odkaz:
http://arxiv.org/abs/1904.12906
Publikováno v:
J. Phys: Conf. Series 1194, (2019),012003
The paper discusses P$_{III-V}$ equation for special values of its parameters for which this equation reduces to P$_{III}$, I$_{12}$, as well as, to some special cases of I$_{38}$ and I$_{49}$ equations from the Ince's list of $50$ second order diffe
Externí odkaz:
http://arxiv.org/abs/1904.11791
Publikováno v:
J. Phys A:Math. Theor. 52,(2019) 065203
We review the construction of the mixed Painlev\'e P$_{III-V}$ system in terms of a 4-boson integrable model and discuss its symmetries. Such a mixed system consist of an hybrid differential equation that for special limits of its parameters reduces
Externí odkaz:
http://arxiv.org/abs/1811.00495