Preface to the special issue: Orthogonal polynomials and integrable systems, Peakons, Toda lattices and Painlevé transcendents

Abstract

Since the 1990s, the theory of orthogonal polynomials has been increasingly playing an essential role in integrable systems, in particular Toda type lattices, peakon dynamical systems of Camassa–Holm (CH) type, as well as Random Matrix theory, and Painlevé Transcendents. This special issue focuses on recent advances in these areas. Still, in addition to research papers, it also includes review articles providing an overview of the pertinent developments which have impacted the synergy of the theory of integrable systems, approximation theory, and the theory of orthogonal polynomials and generalizations.