Related papers: Bispectral Operators, Dual Isomonodromic Deformati…
Integrable deformations of a class of Rikitake dynamical systems are constructed by deforming their underlying Lie-Poisson Hamiltonian structures, which are considered linearizations of Poisson--Lie structures on certain (dual) Lie groups.…
In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a $\tau$-function of the sixth Painlev\'e system by constructing an associated isomonodromic system within their theory of…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
We define a bi-directional embedding between hypersequent calculi and a subclass of systems of rules (2-systems). In addition to showing that the two proof frameworks have the same expressive power, the embedding allows for the recovery of…
This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference…
Pseudo-harmonic morphisms give rise on the domain space to a distribution which admits an almost complex structure compatible with the given Riemannian metric. We shall show that this property, together with the harmonicity, are preserved…
We describe a simple algebraic approach to several spectral duality results for integrable systems and illustrate the method for two types of examples: The Bertola-Eynard-Harnad spectral duality of the two-matrix model as well as the…
These lectures introduce the method of nonlinear steepest descent for Riemann-Hilbert problems. This method finds use in studying asymptotics associated to a variety of special functions such as the Painlev\'{e} equations and orthogonal…
In the first part of the paper we present the dressing method which generates multi-soliton solutions to integrable systems of nonlinear partial differential equations. We compare the approach of Neugebauer with that of Zakharov, Shabat and…
We present a new construction for obtaining pairs of higher-step isospectral Riemannian nilmanifolds and compare several resulting new examples. In particular, we present new examples of manifolds that are isospectral on functions, but not…
A general scheme for determining and studying integrable deformations of algebraic curves is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of…
We develop the Inverse Scattering Transform (IST) method for the Degasperis-Procesi equation. The spectral problem is an $\mathfrak{sl}(3)$ Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
We define the concept of a bi-operad. We develop the homotopy theory of "Bital-Sets" and of infinite-bi-operads. We develop a geometry of generalized schemes based on the spectra of distributive monochromatic bi-operads.
We display methods that allow for computations of spectra, pseudospectra and resolvents of linear operators on Hilbert spaces and also elements in unital Banach algebras. The paper considers two different approaches, namely, pseudospectral…
In image set classification, a considerable advance has been made by modeling the original image sets by second order statistics or linear subspace, which typically lie on the Riemannian manifold. Specifically, they are Symmetric Positive…
In this paper we describe various applications of the Riemann-Hilbert method to the theory of orthogonal polynomials on the line and on the circle.
The soliton solutions of the Degasperis-Procesi equations are constructed by the implementation of the dressing method. The form of the one and two soliton solutions coincides with the form obtained by Hirota's method.
Given a closed complex manifold $X$ of even dimension, we develop a systematic (vertex) algebraic approach to study the rational orbifold cohomology rings $\orbsym$ of the symmetric products. We present constructions and establish results…
We introduce a dbar-formulation of the orthogonal polynomials on the complex plane, and hence of the related normal matrix model, which is expected to play the same role as the Riemann-Hilbert formalism in the theory of orthogonal…