Superposition Formulae for the Geometric Bäcklund Transformations of the Hyperbolic and Elliptic Sine-Gordon and Sinh-Gordon Equations

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Kelmer, Filipe, Tenenblat, Keti
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212108
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Superposition Formulae for the Geometric Bäcklund Transformations of the Hyperbolic and Elliptic Sine-Gordon and Sinh-Gordon Equations. Filipe Kelmer and Keti Tenenblat. SIGMA 20 (2024), 015, 27 pages

We provide superposition formulae for the six cases of Bäcklund transformations corresponding to space-like and time-like surfaces in the 3-dimensional pseudo-Euclidean space. In each case, the surfaces have constant negative or positive Gaussian curvature, and they correspond to solutions of one of...