Skew-orthogonal polynomials (SOPs) arise in the study of the n-point distribution function for
orthogonal and symplectic random matrix ensembles. Motivated by the average of …

This paper focuses on different reductions of the two-dimensional (2d)-Toda hierarchy.
Symmetric and skew-symmetric moment matrices are first considered, resulting in differential …

In this paper, we propose a finite Toda lattice of CKP type (C-Toda) together with a Lax pair.
Our motivation is based on the fact that the Camassa–Holm (CH) peakon dynamical system …

Abstract The Bures–Hall ensemble is a unique measure of density matrices that satisfies
various distinguished properties in quantum information processing. In this work, we study …

We consider an ensemble of random density matrices distributed according to the Bures
measure. The corresponding joint probability density of eigenvalues is described by the …

This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable
hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting …

Inspired by Okounkov's work (2001)[20] which relates KP hierarchy to determinant point
process, we establish a relationship between BKP hierarchy and Pfaffian point process. We …

The solitons solution of BKP equation can be constructed by the Pfaffian structure. Then one
investigates the real line solitons structure of BKP equation using the totally non-negative …

This paper deals with localized waves in the (2+ 1)-dimensional Caudrey-Dodd-Gibbon-
Kotera-Sawada (CDGKS) equation in the incompressible fluid. Based on Hirota's bilinear …

We simulate a system of coupled kicked tops to generate random density matrices
distributed according to the Bures-Hall measure, which has an important role in quantum …