Zobrazeno 1 - 10
of 363
pro vyhledávání: '"Gomes, J F"'
A systematic construction for supersymmetric negative (non-local) flows for mKdV and KdV based on $sl(2,1)$ with a principal gradation is proposed in this paper. We show that smKdV and sKdV can be mapped onto each other through a gauge super Miura tr
Externí odkaz:
http://arxiv.org/abs/2410.00280
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Proceedings: OCNMP Conference, Bad Ems (Germany), 23-29 June 2024 (April 26, 2024) ocnmp:13294
The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (flows) which shares a common affine Lie algebraic structure. The integr
Externí odkaz:
http://arxiv.org/abs/2403.16285
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:
Braz J Phys 53, 24 (2023)
A systematic construction of a class of integrable hierarchy is discussed in terms of the twisted affine $A_{2r}^{(2)}$ Lie algebra. The zero curvature representation of the time evolution equations are shown to be classified according to its algebra
Externí odkaz:
http://arxiv.org/abs/2206.02018
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),435201
The construction of Miura and B\"acklund transformations for $A_n$ mKdV and KdV hierarchies are presented in terms of gauge transformations acting upon the zero curvature representation. As in the well known $sl(2)$ case, we derive and relate the equ
Externí odkaz:
http://arxiv.org/abs/2106.00741
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