Introduces the spectral and inverse spectral theory of Jacobi operators and applications of
these theories to the Toda and Kac-van Moerbeke hierarchy. The author investigates the …

Any logical procedure that is used to reason or to infer either deductively or inductively, so
as to draw conclusions or make decisions, can be called, in a broad sense, a realization …

Abstract The Camassa–Holm hierarchy can be regarded as isospectral flows of the
inhomogeneous string. This paper is devoted to the exploration of the second flow in the …

In this work, we propose a new approach called``stationary reduction method based on
nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlev\'{e}-type …

A one-parameter deformation of the measure of orthogonality for orthogonal polynomials on
the unit circle is considered. The corresponding dynamics of the Schur parameters of the …

We consider matrix Toda and Volterra lattice equations and their relation with matrix
biorthogonal polynomials. From that relation, we give a method for constructing a new …

In this paper we present multidimensional analogues of both the continuous-and discrete-
time Toda lattices. The integrable systems that we consider here have two or more space …

A characterization of classical and semiclassical orthogonal polynomials from their dual
polynomials - ScienceDirect Skip to main contentSkip to article Elsevier logo Journals & …

Firstly, a formal correspondence is established between the Camassa–Holm (CH) equation
and a two-component modified CH (or called SQQ) equation according to the method of …

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