Related papers: Discrete integrable systems and Pitman's transform…
We establish a correspondence between an infinite set of special solutions of the (classical) modified sinh-Gordon equation and a set of stationary states in the finite-volume Hilbert space of the integrable 2D QFT invented by V.A. Fateev.…
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 coordinates. To construct the systems, we generalize the…
We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six…
We present a study of a quasi-integrable deformation of the three-particle open Toda chain, constructed by introducing a translation-invariant three-body interaction terms. Although this modification explicitly breaks the exact…
We study an integrable system related to the relativistic Toda lattice. The bilinear representation of this lattice is given and the B\"ackulund transformation obtained. A fully discrete version is also introduced with its bilinear…
The author discusses integrability of Hamiltonian dynamical systems in the aftermath of KdV. The author also discusses the role of integrable systems in certain numerical computations, particularly the computation of the eigenvalues of a…
Second order integrals of motion for 3d quantum mechanical systems with position dependent masses (PDM) are classified. Namely, all PDM systems are specified which, in addition to their rotation invariance, admit at least one second order…
A novel approach is proposed to characterize the dynamics of perturbed many-body integrable systems. Focusing on the paradigmatic case of the Toda chain under non-integrable Hamiltonian perturbations, this study introduces a method based…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2+1 dimensions, such as the dispersionless Kadomtsev-Petviashvili (dKP) and dispersionless Toda lattice (dTl) equations, can be deformed into reductions of…
We investigate the relation between the local variables of a discrete integrable lattice system and the corresponding separation variables, derived from the associated spectral curve. In particular, we have shown how the inverse…
The knowledge of {\it non usual} and sometimes {\it hidden} symmetries of (classical) integrable systems provides a very powerful setting-out of solutions of these models. Primarily, the understanding and possibly the quantisation of…
We establish an intriguing correspondence between a special set of classical solutions of the modified sinh-Gordon equation (i.e., Hitchin's "self-duality" equations) on a punctured Riemann sphere and a set of stationary states in the…
The quest to reveal the physical essence of the infinitely many symmetries and conservation laws that are intrinsic to integrable systems has historically posed a significant challenge at the confluence of physics and mathematics. This…
We present the constraint for the discrete Moutard equation which gives the integrable discretization of the Bianchi-Ernst system. We also derive the discrete analogue of the Bianchi transformation between solutions of such a system (the…
A dynamical system with discrete time is studied by means of algebraic geometry. The system admits a reduction that is interpreted as a classical field theory in 2+1-dimensional wholly discrete space-time. The integrals of motion of a…
The relation between the infinite-dimensional 3-algebras and the dispersionless KdV hierarchy is investigated. Based on the infinite-dimensional 3-algebras, we derive two compatible Nambu Hamiltonian structures. Then the dispersionless KdV…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known equations such as the Korteweg--de Vries, coupled KdV, Harry…
We construct generalized solutions to the ultradiscrete KdV equation, including the so-called negative solition solutions. The method is based on the ultradiscretization of soliton solutions to the discrete KdV equation with gauge…