WK Schief - Journal of Nonlinear Mathematical Physics, 2003 - Taylor & Francis
Möbius invariant versions of the discrete Darboux, KP, BKP and CKP equations are derived by imposing elementary geometric constraints on an (irregular) lattice in a three-dimensional …
A Doliwa - Proceedings of the Royal Society A …, 2010 - royalsocietypublishing.org
We study the Desargues maps, which generate lattices whose points are collinear with all their nearest (in positive directions) neighbours. The multi-dimensional compatibility of the …
We show that solution to the Hermite–Padé type I approximation problem leads in a natural way to a subclass of solutions of the Hirota (discrete Kadomtsev–Petviashvili) system and of …
A new field of discrete differential geometry is presently emerging on the border between differential and discrete geometry. Whereas classical differential geometry investigates …
A Doliwa - Journal of Physics A: Mathematical and Theoretical, 2013 - iopscience.iop.org
We introduce integrable multicomponent non-commutative lattice systems, which can be considered as analogues of the modified Gel'fand–Dikii hierarchy. We present the …
A Doliwa, P Grinevich, M Nieszporski… - Journal of mathematical …, 2007 - pubs.aip.org
We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of …
Integrable discrete scalar equations defined on a 2D or 3D lattice can be rewritten as difference systems in bond variables or in face variables, respectively. Both the difference …
A Doliwa, SM Sergeev - Journal of Mathematical Physics, 2014 - pubs.aip.org
D is an arbitrary division ring (skew field), associated with the Veblen configuration, and we show that such a map provides solutions to the functional dynamical pentagon equation. We …
A Doliwa - Journal of Geometry and Physics, 2007 - Elsevier
The B-quadrilateral lattice (BQL) provides geometric interpretation of Miwa's discrete BKP equation within the quadrialteral lattice (QL) theory. After discussing the projective-geometric …