A 2 × 2 Lax Representation, Associated Family, and Bäcklund Transformation for Circular K-Nets

Tim Hoffmann, Andrew O. Sageman-Furnas

Research output: Contribution to journalArticlepeer-review

Abstract

We present a 2 × 2 Lax representation for discrete circular nets of constant negative Gauß 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 Bäcklund transformations and an associated family. All the members of that family—although no longer circular—can be shown to have constant Gauß curvature as well. Explicit solutions for the Bäcklund transformations of the vacuum (in particular Dini’s surfaces and breather solutions) and their respective associated families are given.

Original languageEnglish
Pages (from-to)472-501
Number of pages30
JournalDiscrete and Computational Geometry
Volume56
Issue number2
DOIs
StatePublished - 1 Sep 2016

Keywords

  • Bäcklund transformations
  • Discrete differential geometry
  • Discrete integrable systems
  • Multidimensional consistency

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