# Complete classification of rational solutions of A2-Painlevé systems

@article{GomezUllate2020CompleteCO, title={Complete classification of rational solutions of A2-Painlev{\'e} systems}, author={David G'omez-Ullate and Yves Grandati and Robert Milson}, journal={Advances in Mathematics}, year={2020} }

## 3 Citations

### An affine Weyl group characterization of polynomial Heisenberg algebras

- MathematicsAnnals of Physics
- 2022

### Exceptional Gegenbauer polynomials via isospectral deformation

- MathematicsStudies in Applied Mathematics
- 2022

In this paper, we show how to construct exceptional orthogonal polynomials (XOP) using isospectral deformations of classical orthogonal polynomials. The construction is based on confluent Darboux…

### The Expansion of Wronskian Hermite Polynomials in the Hermite Basis

- Mathematics
- 2021

We express Wronskian Hermite polynomials in the Hermite basis and obtain an explicit formula for the coefficients. From this we deduce an upper bound for the modulus of the roots in the case of…

## References

SHOWING 1-10 OF 68 REFERENCES

### Cyclic Maya diagrams and rational solutions of higher order Painlevé systems

- MathematicsStudies in Applied Mathematics
- 2020

This paper focuses on the construction of rational solutions for the A2n ‐Painlevé system, also called the Noumi‐Yamada system, which are considered the higher order generalizations of PIV. In this…

### Large-Degree Asymptotics of Rational Painlevé-IV Solutions by the Isomonodromy Method

- MathematicsConstructive Approximation
- 2022

The Painlevé-IV equation has two families of rational solutions generated, respectively, by the generalized Hermite polynomials and the generalized Okamoto polynomials. We apply the isomonodromy…

### Large-Degree Asymptotics of Rational Painlevé-IV Functions Associated to Generalized Hermite Polynomials

- MathematicsInternational Mathematics Research Notices
- 2018

The Painlevé-IV equation has three families of rational solutions generated by the generalized Hermite polynomials. Each family is indexed by two positive integers $m$ and $n$. These functions have…

### Generalized Hermite Polynomials and Monodromy-Free Schrödinger Operators

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2018

We consider a class of monodromy-free \Sch operators with rational potentials constituted by generalized Hermite polynomials. These polynomials defined as Wronskians of classic Hermite polynomials…

### Poles of Painlevé IV Rationals and their Distribution

- Mathematics
- 2018

We study the distribution of singularities (poles and zeros) of rational solutions of the Painleve IV equation by means of the isomonodromic deformation method. Singularities are expressed in terms…

### A Conjecture on Exceptional Orthogonal Polynomials

- MathematicsFoundations of Computational Mathematics
- 2012

Exceptional orthogonal polynomial systems (X-OPSs) arise as eigenfunctions of Sturm–Liouville problems, but without the assumption that an eigenpolynomial of every degree is present. In this sense,…

### Connection between quantum systems involving the fourth Painlevé transcendent and k-step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial

- Physics
- 2015

The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painleve transcendent PIV, obtained in the context of second-order…

### Rational extensions of the quantum harmonic oscillator and exceptional Hermite polynomials

- Mathematics
- 2013

We prove that every rational extension of the quantum harmonic oscillator that is exactly solvable by polynomials is monodromy free, and therefore can be obtained by applying a finite number of…

### Symmetries in the fourth Painlevé equation and Okamoto polynomials

- MathematicsNagoya Mathematical Journal
- 1999

Abstract The fourth Painlevé equation PIV is known to have symmetry of the affine Weyl group of type with respect to the Bäcklund transformations. We introduce a new representation of PIV , called…