Nonlinear hyperbolic equations in surface theory: Integrable discretizations and approximation results

DOI10.1090/S1061-0022-06-00892-2zbMath1098.53005arXivmath/0208042MaRDI QIDQ5481290

Daniel Matthes, Alexander Ivanovich Bobenko, Yuri Borisovich Suris

Publication date: 9 August 2006

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0208042

zbMATH Keywords

sine-Gordon equationGoursat problemdiscrete differential geometryHirota equationconstant negative Gaussian curvaturediscretization of nonlinear hyperbolic system

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Second-order nonlinear hyperbolic equations (35L70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25)

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Generalized Weierstrass representations of surfaces with the constant Gauss curvature in pseudo-Riemannian three-dimensional space forms, On the semidiscrete differential geometry of A-surfaces and K-surfaces, Initial value problems of the sine-Gordon equation and geometric solutions, Constructing Solutions to the Björling Problem for Isothermic Surfaces by Structure Preserving Discretization

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