489 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- Netherlands Institute for Radio AstronomyNL23 papers
- Belarusian State UniversityBY14 papers
- Leibniz Institute for Astrophysics PotsdamDE14 papers
- Polish Academy of SciencesPL14 papers
- Thüringer Landessternwarte TautenburgDE14 papers
- University of ManchesterGB14 papers
- University of WarsawPL14 papers
- Leiden UniversityNL13 papers
- Centre National de la Recherche ScientifiqueFR12 papers
- Radboud University NijmegenNL12 papers
- Rutherford Appleton LaboratoryGB12 papers
- Bielefeld UniversityDE11 papers
30 papers · 1 filter
Determinantal approach to multiple orthogonal polynomials, and the corresponding integrable equations
Adam Doliwa
We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite-Padé ap…
Bäcklund transformations as integrable discretization. The geometric approach
Adam Doliwa
We present interpretation of known results in the theory of discrete asymptotic and discrete conjugate nets from the "discretization by Bäcklund transformations" point of view. We…
Non-autonomous multidimensional Toda system and multiple interpolation problem
Adam Doliwa
We study the interpolation analogue of the Hermite-Padé type I approximation problem. We provide its determinant solution and we write down the corresponding integrable discrete sy…
Non-commutative Hermite--Padé approximation and integrability
Adam Doliwa
We introduce and solve the non-commutative version of the Hermite-Padé type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to a subcl…
Discrete Darboux system with self-consistent sources and its symmetric reduction
Adam Doliwa, Runliang Lin, Zhe Wang
The discrete non-commutative Darboux system of equations with self-consistent sources is constructed, utilizing both the vectorial fundamental (binary Darboux) transformation and t…
Non-commutative bi-rational maps satisfying Zamolodchikov equation, and Desargues lattices
Adam Doliwa, Rinat M. Kashaev
We present new solutions of the functional Zamolodchikov tetrahedron equation in terms of birational maps in totally non-commutative variables. All the maps originate from Desargue…
The Coxeter relations and KP map for non-commuting symbols
Adam Doliwa, Masatoshi Noumi
We give an action of the symmetric group on non-commuting indeterminates in terms of series in the corresponding Mal'cev-Newmann division ring. The action is constructed from the n…
Non-commutative double-sided continued fractions
Adam Doliwa
We study double-sided continued fractions whose coefficients are non-commuting symbols. We work within the formal approach of the Mal'cev-Neumann series and free division rings. We…
Quadrangular sets in projective line and in Moebius space, and geometric interpretation of the non-commutative discrete Schwarzian Kadomtsev-Petviashvili equation
Adam Doliwa, Jarosław Kosiorek
We present geometric interpretation of the discrete Schwarzian Kadomtsev-Petviashvili equation in terms of quadrangular set of points of a projective line. We give also the corresp…
Non-commutative q-Painleve VI equation
Adam Doliwa
By applying suitable centrality condition to non-commutative non-isospectral lattice modified Gel'fand-Dikii type systems we obtain the corresponding non-autonomous equations. Then…
Discrete KP equation with self-consistent sources
Adam Doliwa, Runliang Lin
We show that the discrete Kadomtsev-Petviashvili (KP) equation with sources obtained recently by the "source generalization" method can be incorporated into the squared eigenfuncti…
Non-commutative rational Yang-Baxter maps
Adam Doliwa
Starting from multidimensional consistency of non-commutative lattice modified Gel'fand-Dikii systems we present the corresponding solutions of the functional (set-theoretic) Yang-…
Desargues maps and their reductions
Adam Doliwa
We present recent developments on geometric theory of the Hirota system and of the non-commutative discrete Kadomtsev-Petviashvili (KP) hierarchy adding also some new results which…
Non-commutative lattice modified Gel'fand-Dikii systems
Adam Doliwa
We introduce integrable multicomponent non-commutative lattice systems, which can be considered as analogs of the modified Gel'fand-Dikii hierarchy. We present the corresponding sy…
Hirota equation and the quantum plane
Adam Doliwa
We discuss geometric integrability of Hirota's discrete KP equation in the framework of projective geometry over division rings using the recently introduced notion of Desargues ma…
The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system
Adam Doliwa
We study recently introduced Desargues maps, which provide simple geometric interpretation of the non-commutative Hirota--Miwa system. We characterize them as maps of the A-type ro…
Desargues maps and the Hirota-Miwa equation
Adam Doliwa
We study the Desargues maps $ϕ:\ZZ^N\to\PP^M$, which generate lattices whose points are collinear with all their nearest (in positive directions) neighbours. The multidimensional c…
Darboux transformations for linear operators on two dimensional regular lattices
Adam Doliwa, Maciej Nieszporski
Darboux transformations for linear operators on regular two dimensional lattices are reviewed. The six point scheme is considered as the master linear problem, whose various specif…
On -function of the quadrilateral lattice
Adam Doliwa
We investigate the -function of the quadrilateral lattice using the nonlocal -dressing method, and we show that it can be identified with the Fredholm determinant…
The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction
Adam Doliwa
The C-quadrilateral lattice (CQL), called also the symmetric lattice, provides geometric interpretation of the discrete CKP equation within the quadrilateral lattice (QL) theory. W…
Integrable dynamics of Toda-type on the square and triangular lattices
Paolo Maria Santini, Adam Doliwa, Maciej Nieszporski
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 o…
Integrable lattices and their sublattices II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices
A. Doliwa, M. Nieszporski, P. M. Santini
An integrable self-adjoint 7-point scheme on the triangular lattice and an integrable self-adjoint scheme on the honeycomb lattice are studied using the sublattice approach. The st…
The B-quadrilateral lattice, its transformations and the algebro-geometric construction
Adam Doliwa
The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-ge…
Integrable Systems and Discrete Geometry
A. Doliwa, P. M. Santini
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.