Sep 14 – 16, 2020
SISSA
Europe/Rome timezone

Matrix generalization of the PII hierarchy: Lax pair and solutions in terms of Fredholm determinants.

Sep 14, 2020, 12:00 PM
30m
Chairman: Davide Guzzetti

Chairman: Davide Guzzetti

Scientific Programme

Speaker

Sofia Tarricone (Université d'Angers/Concordia University )

Description

This talk is focused on some properties of a matrix generalization of the Painlev´e II hierarchy. In particular, we consider Fredholm determinants of matrix convolution operators associated to matrix versions of the n−th Airy functions. Using the theory of integrable operators, we relate them to a fully noncommutative Painlev´e II hierarchy, defined through a matrix valued version of the Lenard operators. In particular we show how to find a matrix valued Lax pair of this hierarchy and, as by product, how to obtain solutions in terms of the Fredholm determinants above. (https://arxiv.org/abs/2007.05707)

Primary author

Sofia Tarricone (Université d'Angers/Concordia University )

Presentation materials