相关论文: On the singularity structure of the discrete KdV e…

We study the structure of singularities in the discrete Korteweg-deVries (d-KdV) equation. Four different types of singularities are identified. The first type corresponds to localised, `confined', singularities, the confinement constraints…

We examine the validity of the results obtained with the singularity confinement integrability criterion in the case of discrete Painlev\'e equations. The method used is based on the requirement of non-exponential growth of the homogeneous…

The deautonomisation of birational maps that have the singularity confinement property, i.e. the construction of nonautonomous versions of such maps that preserve the singularity properties of the original, has proven crucial in our…

We describe the various types of singularities that can arise for second order rational mappings and we discuss the historical and present-day, practical, role the singularity confinement property plays as an integrability detector. In…

We study the distribution of singularities for partial difference equations, in particular, the bilinear and nonlinear form of the discrete version of the Korteweg-de Vries (dKdV) equation. By the Laurent property, the irreducibility, and…

We study singularity confinement phenomena in examples of delay-differential Painlev\'e equations, which involve shifts and derivatives with respect to a single independent variable. We propose a geometric interpretation of our results in…

We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a…

We study the singularities of a modified lattice Korteweg-deVries (KdV) equation and show that it admits three families of singularities, with analogous properties to those found in the lattice KdV equation. The first family consists of…

We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…

Discrete dynamical systems over finite fields are investigated and their integrability is discussed. In particular, the discrete Painlev\'{e} equations and the discrete KdV equation are defined over finite fields and their special solutions…

Hirota's discrete Korteweg-de Vries equation (dKdV) is an integrable partial difference equation on 2-dimensional integer lattice, which approaches the Korteweg-de Vries equation in a continuum limit. We find new transformations to other…

We confront two integrability criteria for rational mappings. The first is the singularity confinement based on the requirement that every singularity, spontaneously appearing during the iteration of a mapping, disappear after some steps.…

A class of discrete equations is considered from three perspectives corresponding to three measures of the complexity of solutions: the (hyper-) order of meromorphic solutions in the sense of Nevanlinna, the degree growth of iterates over a…

We present a new approach to singularity confinement which makes it an efficient and reliable discrete integrability detector. Our method is based on the full-deautonomisation procedure, which consists in analysing non-autonomous extensions…

Asymptotic stability is with no doubts an essential property to be studied for any system. This analysis often becomes very difficult for coupled systems and even harder when different timescales appear. The singular perturbation method…

We investigate some of the discrete Painleve equations (dPII, qPI and qPII) and the discrete KdV equation over finite fields. The first part concerns the discrete Painleve equations. We review some of the ideas introduced in our previous…

We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…

Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved…

We study the analytic properties of a matrix discrete system introduced in [7]. The singularity confinement for this system is shown to hold generically, i.e. in the whole space of parameters except possibly for algebraic subvarieties. This…

We introduce an equation defined on a multi-dimensional lattice, which can be considered as an extension to the coprimeness-preserving discrete KdV like equation in our previous paper. The equation is also interpreted as a…