Related papers: Reductions of integrable lattices
We give explicit formulas for resistance distance matrices and Moore-Penrose inverses of incidence and Laplacian matrices of ladder, circular ladder, and M\"{o}bius ladder graphs. As a result, we compute the Kirchhoff index of these graphs…
We show that there exists an alternative procedure in order to extract differential hierarchies, such as the KdV hierarchy, from one--matrix models, without taking a continuum limit. To prove this we introduce the Toda lattice and…
We investigate properties of closed approximate subgroups of locally compact groups, with a particular interest for approximate lattices i.e. those approximate subgroups that are discrete and have finite co-volume. We prove an approximate…
We define the coupled modified KP hierarchy and its dispersionless limit. This integrable hierarchy is a generalization of the ''half'' of the Toda lattice hierarchy as well as an extension of the mKP hierarchy. The solutions are…
We announce various results concerning the structure of compactly generated simple locally compact groups. We introduce a local invariant, called the structure lattice, which consists of commensurability classes of compact subgroups with…
All Darboux integrable difference equations on the quad-graph are described in the case of the equations that possess autonomous first-order integrals in one of the characteristics. A generalization of the discrete Liouville equation is…
We derive formulas and algorithms for Kitaev's invariants in the periodic table for topological insulators and superconductors for finite disordered systems on lattices with boundaries. We find that K-theory arises as an obstruction to…
A new class of integrable maps, obtained as lattice versions of polynomial dynamical systems is introduced. These systems are obtained by means of a discretization procedure that preserves several analytic and algebraic properties of a…
A systematic reformulation of the KP hierarchy by using continuous Miwa variables is presented. Basic quantities and relations are defined and determinantal expressions for Fay's identities are obtained. It is shown that in terms of these…
We present a generalization of Dirac constraint theory based on the theory of Poisson-Dirac submanifolds. The theory is formulated in a coordinate-free manner while simultaneously relaxing the invertibility condition as seen in standard…
A new infinite set of commuting additional (``ghost'') symmetries is proposed for the KP-type integrable hierarchy. These symmetries allow for a Lax representation in which they are realized as standard isospectral flows. This gives rise to…
We propose a construction of lattices from codes corresponding to lattices of type $A_n$, $D_n$ and $E_n$. This construction is a generalization of construction A of lattices from $p$-ary codes corresponding to a lattice of type $A_{p-1}$.…
The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with…
The problem of construction of the boundary conditions for the Toda lattice compatible with its higher symmetries is considered. It is demonstrated that this problem is reduced to finding of the differential constraints consistent with the…
A hierarchy of integrable hamiltonian nonlinear ODEs is associated with any decomposition of the Lie algebra of Laurent series with coefficients being elements of a semi-simple Lie algebra into a sum of the subalgebra consisting of the…
Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four parameter class of reflectionless systems. Their potentials correspond to composition of…
In this paper we derive new two-component integrable differential difference and partial difference systems by applying a Lax-Darboux scheme to an operator formed from an ${\mathfrak{sl}}_3({\mathbb{C}})$-based automorphic Lie algebra. The…
Let G be a topological Kac-Moody group of rank 2 with symmetric Cartan matrix, defined over a finite field F_q. An example is G = SL(2,F_q((t^{-1}))). We determine a positive lower bound on the covolumes of cocompact lattices in G, and…
Let $L$ be a finite lattice and let $I$ be an ideal of $L$. Then the restriction map is a bounded lattice homomorphism of the congruence lattice of~$L$ into the congruence lattice of $I$. In a 2009 paper, the authors proved the converse. In…
We study the discretization of Darboux integrable systems. The discretization is done using $x$-, $y$-integrals of the considered continuous systems. New examples of semi-discrete Darboux integrable systems are obtained.