5 citations · 9 across the 3 of their papers we have counts for
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Geometric algebra and quadrilateral lattices
Adam Doliwa
Motivated by the fundamental results of the geometric algebra we study quadrilateral lattices in projective spaces over division rings. After giving the noncommutative discrete Dar…
Integrable lattices and their sub-lattices: from the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme
A. Doliwa, P. Grinevich, M. Nieszporski +1
We introduce the sub-lattice approach, a procedure to generate, from a given integrable lattice, a sub-lattice which inherits its integrability features. We consider, as illustrati…
An integrable generalization of the Toda law to the square lattice
P. M. Santini, M. Nieszporski, A. Doliwa
We generalize the Toda lattice (or Toda chain) equation to the square lattice; i.e., we construct an integrable nonlinear equation, for a scalar field taking values on the square l…
The normal dual congruences and the dual Bianchi lattice
Adam Doliwa
The main goal of this paper is to find the discrete analogue of the Bianchi system in spaces of arbitrary dimesion together with its geometric interpretation. We show that the prop…
Geometric discretization of the Bianchi system
A. Doliwa, M. Nieszporski, P. M. Santini
We introduce the dual Koenigs lattices, which are the integrable discrete analogues of conjugate nets with equal tangential invariants, and we find the corresponding reduction of t…
Algebro-geometric solution of the discrete KP equation over a finite field out of a hyperelliptic curve
M. Bialecki, A. Doliwa
We transfer the algebro-geometric method of construction of solutions of the discrete KP equation to the finite field case. We emphasize role of the Jacobian of the underlying alge…