Superposition formulae for the geometric Bäcklund transformations of the hyperbolic and elliptic sine-Gordon and sinh-Gordon equations

arXiv2211.01247MaRDI QIDQ6196821

Filipe Kelmer, Keti Tenenblat

Publication date: 15 March 2024

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.01247

zbMATH Keywords

sine-Gordon equationBäcklund transformationsinh-Gordon equationsurfaces in the 3-dimensional pseudo-Euclidean space

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Surfaces in Euclidean and related spaces (53A05) Second-order hyperbolic equations (35L10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Totally quasi-umbilic timelike surfaces in \(\mathbb{R}^{1,2}\)
• Isometric immersions of pseudo-Riemannian space forms
• Spectral analysis of the elliptic sine-Gordon equation in the quarter plane
• Submanifolds of constant sectional curvature in pseudo-Riemannian manifolds
• A higher dimension generalization of the Sine-Gordon equation and its soliton theory
• Bäcklund's theorem for \(n\)-dimensional submanifolds of \(R^{2n-1}\)
• Boundary-value problem for the two-dimensional elliptic sine-Gordon equation and its application to the theory of the stationary Josephson effect
• Bäcklund transformations for a class of systems of differential equations
• Bäcklund transformation on surfaces with \(K=-1\) in \(\mathbb{R}^{2,1}\)
• On time-like surfaces of positive constant Gaussian curvature and imaginary principal curvatures
• Boundary value problems for the elliptic sine-Gordon equation in a semi-strip
• Nonlinear-Evolution Equations of Physical Significance
• Bäcklund transformations for surfaces in Minkowski space
• Direct and inverse scattering problem associated with the elliptic sinh-Gordon equation
• Bäcklund's theorem for submanifolds of space forms and a generalized wave equation

This page was built for publication: Superposition formulae for the geometric Bäcklund transformations of the hyperbolic and elliptic sine-Gordon and sinh-Gordon equations