Related papers: Exactly solvable periodic Darboux q-chains
Nonlinear semi-discrete equations of the form t_x(n+1)=f(t(n), t(n+1), t_x(n)) are studied. An adequate algebraic formulation of the Darboux integrability is discussed and the attempt to adopt this notion to the classification of Darboux…
In this paper, we present the (p; q)-analogues of some inequalities concerning the digamma function. Our results generalize some earlier results.
We develop a search algorithm for systems of $q$-difference equations satisfied by Andrews-Gordon type double series. We then couple the search algorithm with Euler's algorithm for finding infinite products to narrow the search space. We…
We show that any multi-component matrix KP hierarchy is equivalent to the standard one-component (scalar) KP hierarchy endowed with a special infinite set of abelian additional symmetries, generated by squared eigenfunction potentials. This…
In this note we show that various natural q-analogues of the Catalan numbers can be obtained in a uniform way. Furthermore we compute their Hankel determinants.
A $\mathbb Q$-conic bundle is a proper morphism from a threefold with only terminal singularities to a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We study the structure of $\mathbb…
The present paper considers a q-analogue of an operator defined by Erku\c{s}-Duman et al. (Calcolo, 45(1) (2008), 53-67) involving q-Lagrange polynomials in several variables. The Korovkin type theorems in the settings of deferred weighted…
In this paper, we almost completely solve the existence of an almost resolvable cycle system with odd cycle length. We also use almost resolvable cycle systems as well as other combinatorial structures to give some new solutions to the…
We introduce a pair of novel difference equations, whose solutions are expressed in terms of Racah or Wilson polynomials depending on the nature of the finite-difference step. A number of special cases and limit relations are also examined,…
The compatible expansion in series of solutions of both the equations of P-Q pair at neighborhood of the singular point is obtained in closed form for regular and irregular singularities. The conservation laws of the system of ordinary…
For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior…
In this Letter we identify special systems of (an arbitrary number) N of first-order Ordinary Differential Equations with homogeneous polynomials of arbitrary degree M on their right-hand sides, which feature very simple explicit solutions;…
In this paper, we first propose a concept of weighted pseudo-almost periodic functions on time scales and study some basic properties of weighted pseudo-almost periodic functions on time scales. Then, we establish some results about the…
Two binary (integral type) Darboux transformations for the KdV hierarchy with self-consistent sources are proposed. In contrast with the Darboux transformation for the KdV hierarchy, one of the two binary Darboux transformations provides…
We define and study q-delta-matroids, and q-g-matroids. These objects are analogues, for finite-dimensional vector spaces over finite fields, of delta-matroids and g-matroids arising from finite sets. We compare axiomatic descriptions with…
We discuss an integrable discretization of the principal chiral field models equations and its involutive reduction. We present a Darboux transformation and general construction of solution solutions for these discrete equations.
The purpose of this paper is to give symmetric identities for higher-order degenerate q- Bernoulli polynomials arising from the p-adic q-integral on Zp.
In this paper we extend the umbral calculus, developed to deal with difference equations on uniform lattices, to q-difference equations. We show that many of the properties considered for shift invariant difference operators satisfying the…
The q-binomial formula in the limit q->1 is shown to be equivalent to the Rogers five term dilogarithm identity.
We give generalizations and simple proofs of some $q$-identities of Dilcher, Fu and Lascoux related to divisor functions.