相关论文: Classification of integrable Volterra type lattice…
A complete classification of isotropic vector equations of the geometric type that possess higher symmetries is proposed. New examples of integrable multi-component systems of the geometric type and their auto-Backlund transformations are…
The complete lists of vector hyperbolic equations on the sphere that have integrable third order vector isotropic and anisotropic symmetries are presented. Several new integrable hyperbolic vector models are found. By their integrability we…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. For the recently found integrable lattice the hierarchy of symmetries is described. Second and third…
A modification of the symmetry approach for the classification of integrable differential-difference equations of the form $$ u_{n,t} = f_n(u_{n-1}, u_n, u_{n+1}), $$ where $n$ is a discrete integer variable, is presented (the well-known…
The classification of lattice equations that are integrable in the sense of higher-dimensional consistency is extended by allowing directed edges. We find two cases that are not transformable via the 'admissible transformations' to the…
The first part of the book is devoted to the symmetry approach to classification of scalar integrable evolution PDEs with two independent variables. In the second part systems of evolution equations with polynomial homogeneous right-hand…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…
In this paper we study the classification problem of convex lattice ploytopes with respect to given volume or given cardinality.
The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.
Modified Volterra lattice admits two vector generalizations. One of them is studied for the first time. The zero curvature representations, B\"acklund transformations, nonlinear superposition principle and the simplest explicit solutions of…
In this paper a Lotka Volterra type system is considered. For such a system, biHamiltonian formulation, symplectic realizations and symmetries are presented.
A set of vectors all of which have a constant (non-zero) norm value in an Euclidean lattice is called a shell of the lattice. Venkov classified strongly perfect lattices of minimum 3 (R\'{e}seaux et "designs" sph\'{e}rique, 2001), whose…
An approach to master symmetries of lattice equations is proposed by the use of discrete zero curvature equation. Its key is to generate non-isospectral flows from the discrete spectral problem associated with a given lattice equation. A…
Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are…
We consider embeddings of a finite complex in a sphere. We give a homotopy theoretic classification of such embeddings in a wide range.
This paper is devoted to the problem of classification, up to smooth isomorphisms or up to orbital equivalence, of smooth integrable vector fields on 2-dimensional surfaces, under some nondegeneracy conditions. The main continuous…
Generalized symmetry integrability test for discrete equations on the square lattice is studied. Integrability conditions are discussed. A method for searching higher symmetries (including non-autonomous ones) for quad graph equations is…
The Volterra lattice equations are completely integrable and possess bi-Hamiltonian structure. They are integrated using partitioned Lobatto IIIA-B methods which preserve the Poisson structure. Modified equations are derived for the…
The well known Liouville-Arnold theorem says that if a level surface of integrals of an integrable system is compact and connected, then it is a torus. However, in some important examples of integrable systems the topology of a level…