A 2x2 Lax representation, associated family, and B\"acklund transformation for circular K-nets
Abstract
We present a 2x2 Lax representation for discrete circular nets of constant negative Gau curvature. It is tightly linked to the 4D consistency of the Lax representation of discrete K-nets (in asymptotic line parametrization). The description gives rise to B\"acklund transformations and an associated family. All the members of that family -- although no longer circular -- can be shown to have constant Gau curvature as well. Explicit solutions for the B\"acklund transformations of the vacuum (in particular Dini's surfaces and breather solutions) and their respective associated families are given.
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