Related papers: The equivariant Toda lattice, II
In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant-Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n,R). This system was obtained by reducing the space…
We include the relativistic lattice KP hierarchy, introduced by Gibbons and Kupershmidt, into the $r$-matrix framework. An $r$-matrix account of the nonrelativistic lattice KP hierarchy is also provided for the reader's convenience. All…
We investigate the form of equilibrium spatio-temporal correlation functions of conserved quantities, and of energy transport in the Toda lattice and in other integrable models. From numerical simulations we find that the correlations…
Integrable cut-off constraints for semidiscrete Toda lattice are studied in this paper. Lax presentation for semidiscrete analog of the $C$-series Toda lattice is obtained. Nonlocal variables that allow to express symmetries of the infinite…
We construct an integrable hierarchy in terms of vertex operators and Hirota Quadratic Equations (HQE shortly) and we show that the equivariant total descendant potential of $\C P^1$ satisfies the HQE. Our prove is based on the quantization…
Matrix orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss--Borel factorization of two, left and a right, Cantero-Morales-Velazquez block moment matrices, which are…
We study the Pfaff lattice, introduced by us in the context of a Lie algebra splitting of gl(infinity) into sp(infinity) and lower-triangular matrices. We establish a set of bilinear identities, which we show to be equivalent to the Pfaff…
The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems of the ALH can be used to derive a wide…
We study completely integrable Hamiltonian systems whose monodromy matrices are related to the representatives for the set of gauge equivalence classes $\boldsymbol{\mathcal{M}}_F$ of polynomial matrices. Let $X$ be the algebraic curve…
We study elliptic solutions of the recently introduced Toda lattice with the constraint of type B and derive equations of motion for their poles. The dynamics of poles is given by the deformed Ruijsenaars-Schneider system. We find its…
In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…
The simplest nontrivial tau functions of the Toda lattice and the $\tN$-component Toda lattice are compared in their applications to multimatrix integrals.
We develop a systematic procedure of finding integrable ''relativistic'' (regular one-parameter) deformations for integrable lattice systems. Our procedure is based on the integrable time discretizations and consists of three steps. First,…
The Ehrhart polynomial and Ehrhart series count lattice points in integer dilations of a lattice polytope. We introduce and study a $q$-deformation of the Ehrhart series, based on the notions of harmonic spaces and Macaulay's inverse…
We prove that any classical affine W-algebra W(g,f), where g is a classical Lie algebra and f is an arbitrary nilpotent element of g, carries an integrable Hamiltonian hierarchy of Lax type equations. This is based on the theories of…
In this paper we discuss the relation between the functions that give first integrals of full symmetric Toda system (an important Hamilton system on the space of traceless real symmetric matrices) and the vector fields on the group of…
We show that 't Hooft's representation of (2+1)-dimensional gravity in terms of flat polygonal tiles is closely related to a gauge-fixed version of the covariant Hamiltonian lattice theory. 't Hooft's gauge is remarkable in that it leads to…
The exactly integrable systems connected with semisimple series $A$ for arbitrary grading are presented in explicit form. Their general solutions are expressed in terms of the matrix elements of various fundamental representations of $A_n$…
Orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss--Borel factorization of a Cantero-Moral-Velazquez moment matrix, which is constructed in terms of a complex…
In this paper, we construct the additional $W$-symmetry and ghost symmetry of two-lattice field integrable hierarchies. Using the symmetry constraint, we construct constrained two-lattice integrable systems which contain several new…