Nonlinear d'Alembert formula for discrete pseudospherical surfaces

Abstract

On the basis of loop group decompositions (Birkhoff decompositions), we give a discrete version of the nonlinear d'Alembert formula, a method of separation of variables of difference equations, for discrete constant negative Gauss curvature (pseudospherical) surfaces in Euclidean three space. We also compute two examples by this formula in detail.

21 pages, fixed typos (v3)

References in corpus (2)

• Loop Group Decompositions in Almost Split Real Forms and Applications to Soliton Theory and Geometry
• Weierstrass-type Representation of Weakly Regular Pseudospherical Surfaces in Euclidean Space