Related papers: On consistent systems of difference equations
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…
We present a quasi-integrable two-dimensional lattice equation: i.e., a partial difference equation which satisfies a criterion of integrability, singularity confinement, although it has a chaotic aspect in the sense that the degrees of its…
A pluri-Lagrangian (or Lagrangian multiform) structure is an attribute of integrability that has mainly been studied in the context of multidimensionally consistent lattice equations. It unifies multidimensional consistency with the…
We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J. Phys. A ${\bf 43}$ (2010) \& ${\bf 44}$ (2011)]. Together…
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…
In this paper, we present formula solutions of a family of difference equations of higher order. We discuss the periodic nature of the solutions and we investigate the stability character of the equilibrium points. We utilize Lie symmetry…
Lie symmetries of systems of second-order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields. The exact lower and upper bounds for the dimensions of the maximal…
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…
Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of…
Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.
Integrability conditions for difference equations admitting a second order formal recursion operator are presented and the derivation of symmetries and canonical conservation laws is discussed. In the generic case, nonlocal conservation…
Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes…
Dispersive deformations of the Monge equation u_u=uu_x are studied using ideas originating from topological quantum field theory and the deformation quantization programme. It is shown that, to a high-order, the symmetries of the Monge…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
Multidimensional Consistency becomes more and more important in the theory of discrete integrable systems. Recently, we gave a classification of all 3D consistent 6-tuples of equations with the tetrahedron property, where several novel…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
In the paper a two-dimensional integro-differential system is considered. Using some variational methods we give sufficient conditions for the existence and uniqueness of a solution to the considered system. Moreover, we show that the…
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
A relationship between the tetrahedron equation for maps and the consistency property of integrable discrete equations on $\mathbb{Z}^3$ is investigated. Our approach is a generalization of a method developed in the context of Yang-Baxter…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…