178 citations · 609 across the 31 of their papers we have counts for
22 papers · 1 filter
-step rational extensions of the trigonometric Darboux-Pöschl-Teller potential based on para-Jacobi polynomials
Yves Grandati, Christiane Quesne
A previous construction of regular rational extensions of the trigonometric Darboux-Pöschl-Teller potential, obtained by one-step Darboux transformations using seed functions assoc…
Complete classification of rational solutions of -Painlevé systems
David Gómez-Ullate, Yves Grandati, Robert Milson
We provide a complete classification and an explicit representation of rational solutions to the fourth Painlevé equation PIV and its higher order generalizations known as the $A_{…
Rational solutions of Painleve systems
David Gomez-Ullate, Yves Grandati, Robert Milson
Although the solutions of Painlevé equations are transcendental in the sense that they cannot be expressed in terms of known elementary functions, there do exist rational solutions…
Ladder operators and rational extensions
David Gomez-Ullate, Yves Grandati, Zoe McIntyre +1
This note presents the classification of ladder operators corresponding to the class of rational extensions of the harmonic oscillator. We show that it is natural to endow the clas…
Rational solutions of dressing chains and higher order Painleve equations
D. Gomez-Ullate, Y. Grandati, S. Lombardo +1
We present a new approach to determine the rational solutions of the higher order Painleve equations associated to periodic dressing chain systems. We obtain new sets of solutions,…
Cyclic Maya diagrams and rational solutions of higher order Painlevé systems
Peter A. Clarkson, David Gómez-Ullate, Yves Grandati +1
This paper focuses on the construction of rational solutions for the Painlevé system, also called the Noumi-Yamada system, which are considered the higher order generaliza…