77 citations · 177 across the 8 of their papers we have counts for
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A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 - dimensional vector fields
S. V. Manakov, P. M. Santini
We introduce a hierarchy of integrable PDEs in 2+1 dimensions arising from the commutation of 2-dimensional vector fields. We also solve the associated Cauchy problems, using the r…
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 self-adjoint 5-point and 7-point difference operators, the associated Dirichlet problems, Darboux transformations and Lelieuvre formulas
Maciej Nieszporski, Paolo Maria Santini
We present some basic properties of two distinguished discretizations of elliptic operators: the self-adjoint 5-point and 7-point schemes on a two dimensional lattice. We first sho…
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…