108 citations · 1.1k across the 73 of their papers we have counts for
73 papers
Generalized Riemann-Hilbert-Birkhoff Decomposition and a New Class of Higher Grading Integrable Hierarchies
H. Aratyn, C. P. Constantinidis, J. F. Gomes +2
We propose a generalized Riemann-Hilbert-Birkhoff decomposition that expands the standard integrable hierarchy formalism in two fundamental ways: it allows for integer powers of La…
Two-fold degeneracy of a class of rational Painlevé V solutions
H. Aratyn, J. F. Gomes, G. V. Lobo +1
We present a construction of a class of rational solutions of the Painlevé V equation that exhibit a two-fold degeneracy, meaning that there exist two distinct solutions that share…
Why is my rational Painlevé V solution not unique?
H. Aratyn, J. F. Gomes, G. V. Lobo +1
Under special conditions the Painlevé V equation has more than one rational solution solving it with the same parameters. In the setting of formalism that identifies points on orbi…
Derivation of Painlevé type system with affine Weyl group symmetry in a self-similarity limit
H. Aratyn, J. F. Gomes, G. V. Lobo +1
We show how the zero-curvature equations based on a loop algebra of with a principal gradation reduce via self-similarity limit to a polynomial Hamiltonian system of coupled…
On Rational Solutions of Dressing Chains of Even Periodicity
H. Aratyn, J. F. Gomes, G. V. Lobo +1
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)}_…
On Hamiltonian Formalism for Dressing Chain Equations of Even Periodicity
H. Aratyn, J. F. Gomes, A. H. Zimerman
We propose a Hamiltonian formalism for periodic dressing chain with the even number . The formalism is based on Dirac reduction applied to the periodic dressing chain…