TY - JOUR
T1 - A 2 × 2 Lax Representation, Associated Family, and Bäcklund Transformation for Circular K-Nets
AU - Hoffmann, Tim
AU - Sageman-Furnas, Andrew O.
N1 - Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - 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.
AB - 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.
KW - Bäcklund transformations
KW - Discrete differential geometry
KW - Discrete integrable systems
KW - Multidimensional consistency
UR - http://www.scopus.com/inward/record.url?scp=84976417402&partnerID=8YFLogxK
U2 - 10.1007/s00454-016-9802-6
DO - 10.1007/s00454-016-9802-6
M3 - Article
AN - SCOPUS:84976417402
SN - 0179-5376
VL - 56
SP - 472
EP - 501
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
IS - 2
ER -