28 citations · 211 across the 35 of their papers we have counts for
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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…
Extended symmetry of higher Painlevé equations of even periodicity and their rational solutions
Henrik Aratyn, José Francisco Gomes, Gabriel Vieira Lobo +1
The structure of extended affine Weyl symmetry group of higher Painlevé equations of periodicity depends on whether is even or odd. We find that for even , the symmetry…
SKdV, SmKdV flows and their supersymmetric gauge-Miura transformations
Y. F. Adans, A. R. Aguirre, J. F. Gomes +2
The construction of Integrable Hierarchies in terms of zero curvature representation provides a systematic construction for a series of integrable non-linear evolution equations (f…
Comments on the negative grade KdV hierarchy
Y. F. Adans, Jose F. Gomes, G. V. Lobo +1
The construction of negative grade KdV hierarchy is proposed in terms of a Miura-gauge transformation. Such gauge transformation is employed within the zero curvature representatio…
Complex KdV rogue waves from gauge-Miura transformation
Ysla F. Adans, Guilherme França, José F. Gomes +2
The gauge-Miura correspondence establishes a map between the entire KdV and mKdV hierarchies, including positive and also negative flows, from which new relations besides the stand…
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…