Affiliation:
1. Faculty of Mathematics and Computer Science, University of Warmia and Mazury, Ul. Żołnierska 14, 10-561 Olsztyn, Poland
Abstract
We study the Desargues maps
, which generate lattices whose points are collinear with all their nearest (in positive directions) neighbours. The multi-dimensional compatibility of the map is equivalent to the Desargues theorem and its higher dimensional generalizations. The nonlinear counterpart of the map is the non-commutative (in general) Hirota–Miwa system. In the commutative case of the complex field we apply the non-local
-dressing method to construct Desargues maps and the corresponding solutions of the system. In particular, we identify the Fredholm determinant of the integral equation inverting the non-local
-dressing problem with the
τ
-function. Finally, we establish equivalence between the Desargues maps and quadrilateral lattices provided we take into consideration also their Laplace transforms.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
34 articles.
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