The integrable geometric discretization of the Koenigs nets

Adam Doliwa

Instytut Fizyki Teoretycznej, Uniwersytet Warszawski ul. Hoża 69, 00-681 Warszawa, Poland

          e-mail: doliwa@fuw.edu.pl

Abstract

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 Darbouxtype 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.