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 …

In this paper, we propose a complex nonisospectral Schur flow and present its solution
expressed in terms of Toeplitz determinants. In addition, we explore its connection with …

This paper is concerned about certain generalization of Laurent biorthogonal polynomials
together with the corresponding related integrable lattices. On one hand, a generalization for …

For the first two equations of the Volterra lattice hierarchy and the first two equations of its
non-autonomous (non-isospectral) extension, we present Riccati systems for functions cj (t) …

In this paper, we first extend the hungry Lotka–Volterra lattice to a case of nonzero boundary
conditions and present its corresponding exact solution expressed in terms of a block …

In this paper, we mainly consider a combinatoric explanation for block Pfaffians in terms of
non-intersecting paths, as a generalization of results obtained by Stembridge. As …

In this paper, we investigate Laurent biorthogonal polynomials with a weight function of
three parameters, ie $ z^\alpha e^{-t_1z-\frac {t_2}{z}}, z\in (0,+\infty) $, $(t_1> 0,\t_2> …

In this paper, we study a nonisospectral semi-discrete Ablowitz–Kaup–Newell–Segur
equation. Multisoliton solutions for this equation are given by Hirota's method. Dynamics of …

Semiclassical orthogonal polynomials are polynomials orthogonal with respect to
semiclassical weights. The fascinating link between semiclassical orthogonal polynomials …