相关论文: ${\mathbb{Z}}_N$ graded discrete Lax pairs and dis…
A method to generate new classes of random matrix ensembles is proposed. Random matrices from these ensembles are Lax matrices of classically integrable systems with a certain distribution of momenta and coordinates. The existence of an…
In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…
The Lax pair for a derivative nonlinear Schr\"{o}dinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schr\"{o}dinger equations. By virtue of a gauge…
We introduce a class of recursions defined over the $d$-dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation. We shall prove that the equations…
We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding transfer matrices give rise to time evolution equations for the initial Lax…
We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators…
The article studies a class of integrable semidiscrete equations with one continuous and two discrete independent variables. Miura type transformations are obtained that relate the equations of the class. A new integrable chain of this type…
We use a recently proposed scheme of matrix extension of dispersionless integrable systems for the Abelian case, in which it leads to linear equations, connected with the initial dispersionless system. In the examples considered, these…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
We propose a discrete surface theory in $\mathbb R^3$ that unites the most prevalent versions of discrete special parametrizations. This theory encapsulates a large class of discrete surfaces given by a Lax representation and, in…
In the first part of the paper, we classify linear integrable (multi-dimensionally consistent) quad-equations on bipartite isoradial quad-graphs in $\mathbb C$, enjoying natural symmetries and the property that the restriction of their…
In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. In this paper we construct other examples of integrable dynamics of Toda-type on the square lattice, as well as on the triangular lattice,…
We propose the new generalization of linear stationary dynamical systems with discrete time $t\in\mathbb{Z}$ to the case $t\in\nspace{Z}{N}$. The dynamics of such a system can be reproduced by means of its associated multiparametric…
We study properties of Hamiltonian integrable systems with random initial data by considering their Lax representation. Specifically, we investigate the spectral behaviour of the corresponding Lax matrices when the number $N$ of degrees of…
A pedagogical presentation of integrable models with special reference to the Toda lattice hierarchy has been attempted. The example of the KdV equation has been studied in detail, beginning with the infinite conserved quantities and going…
Lax pairs are a useful tool in finding conserved quantities of some dynamical systems. In this expository article, we give a motivated introduction to the idea of a Lax pair of matrices $(L,A)$, first for mechanical systems such as the…
Lax pairs with operator valued coefficients, which are explicitly connected by means of an additional condition, are considered. This condition is proved to be covariant with respect to the Darboux transformation of a general form.…
We review and study the correspondence between discrete linear lattice/chain models of interacting particles and their continuous counterparts represented by linear partial differential equations. In particular, we study the correspondence…
We present the Lax pair formalism for certain extension of the continuous limit of the classical Toda lattice hierarchy, provide a well defined notion of tau function for its solutions, and give an explicit formulation of the relationship…
There are different methods of discretizing integrable systems. We consider semi-discrete analog of two-dimensional Toda lattices associated to the Cartan matrices of simple Lie algebras that was proposed by Habibullin in 2011. This…