Related papers: Selected Topics in Classical Integrability
A construction of conservation laws for chiral models (generalized sigma-models on a two-dimensional space-time continuum using differential forms is extended in such a way that it also comprises corresponding discrete versions. This is…
Here we briefly describe some topics along the lines of projective spaces and related geometric constructions connected to linear algebra, which provide fundamental examples in classical geometry and analysis.
This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…
A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…
A classical model of gravity theory with several dilatonic scalar fields and differential forms admitting an interpretation in terms of intersecting p-branes is studied in (pseudo)-Riemannian space-time $M =R_+\times S^{d_0}\times R_t\times…
In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the…
A multi-component semi-discrete nonlinear integrable system associated with the relevant third-order auxiliary linear problem is claimed to be the prototype system for several reduced integrable systems formulated in terms of true dynamical…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…
The massive phase of two-layer integrable systems is studied by means of RSOS restrictions of affine Toda theories. A general classification of all possible integrable perturbations of coupled minimal models is pursued by an analysis of the…
The purpose of this paper is to construct a generalized r-matrix structure of finite dimensional systems and an approach to obtain the algebro-geometric solutions of integrable nonlinear evolution equations (NLEEs). Our starting point is a…
A number of characteristics of integrable nonlinear partial differential equations (PDE's) for classical fields are reviewed, such as Backlund transformations, Lax pairs, and infinite sequences of conservation laws. An algebraic approach to…
Brief review of the methods for solving the multicomponent nonlinear Schrodinger (MNLS) equations and analysis of their Hamiltonian structures is given. Main attention is paid to the MNLS related to the C.II- and D.III-types symmetric…
The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…
A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical close to TC model [7] is presented.…
This is an introductory survey written in Japanese on classical integrability from the viewpoint of symmetry reduction of 4-dimensional anti-self-dual Yang-Mills equations. Twistor construction methods are discussed in detail in…
Determining whether a dynamical system is integrable is generally a difficult task which is currently done on a case by case basis requiring large human input. Here we propose and test an automated method to search for the existence of…
New integrable lattice systems are introduced, their different integrable discretization are obtained. B\"acklund transformations between these new systems and the relativistic Toda lattice (in the both continuous and discrete time…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in this respect, namely quad-graphs, the cellular…