5 citations · 5 across the 2 of their papers we have counts for
5 papers
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…
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…
The integrable discretization of the Bianchi-Ernst system
M. Nieszporski, A. Doliwa, P. M. Santini
We present the constraint for the discrete Moutard equation which gives the integrable discretization of the Bianchi-Ernst system. We also derive the discrete analogue of the Bianc…
Integrable Discrete Geometry: the Quadrilateral Lattice, its Transformations and Reductions
Adam Doliwa, Paolo Maria Santini
We review recent results on Integrable Discrete Geometry. It turns out that most of the known (continuous and/or discrete) integrable systems are particular symmetries of the quadr…
Lattice geometry of the Hirota equation
Adam Doliwa
Geometric interpretation of the Hirota equation is presented as equation describing the Laplace sequence of two-dimensional quadrilateral lattices. Different forms of the equation…