Adam Doliwa

Instytut Fizyki Teoretycznej, Uniwersytet Warszawski
ul. Hoża 69, 00-681 Warszawa, Poland
e-mail: doliwa@fuw.edu.p


The integrable geometric discretization of the Koenigs nets 

We introduce the Koenigs lattice, which is new integrable 
reduction of the quadrilateral lattice (discrete conjugate net). 
The discretization is performed by the natural extension of the basic 
geometric properties of the Koenigs net to the discrete level.
We construct also the Darboux-type transformation of the Koenigs 
lattice and we show permutability of superpositions of such transformations, 
thus proving integrability of the Koenigs lattice. Details can be found 
in nlin.SI/0203011.