11 citations · 17 across the 8 of their papers we have counts for
8 papers
Volterra-Bogoyavlensky lattices and solutions of invariant Painlevé equations
Y. F. Adans, H. Aratyn, J. F. Gomes +1
The objective of this work is to develop a framework that exploits the lattice structure of the -th Volterra--Bogoyavlensky equations (, ) to generate ration…
New negative grade solitonic sector for supersymmetric KdV and mKdV hierarchies
Y. F. Adans, A. R. Aguirre, J. F. Gomes +2
A systematic construction for supersymmetric negative graded (non-local) flows for mKdV and KdV based on with a principal gradation is proposed in this paper. We show tha…
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…
Negative flows of generalized KdV and mKdV hierarchies and their gauge-Miura transformations
Ysla F. Adans, Guilherme França, José F. Gomes +2
The KdV hierarchy is a paradigmatic example of the rich mathematical structure underlying integrable systems and has far-reaching connections in several areas of theoretical physic…
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)}_…