A generalized formula for integrable classes of surfaces in Lie algebras

DOI10.1063/1.532093zbMath0893.53003OpenAlexW2101562683WikidataQ126199984 ScholiaQ126199984MaRDI QIDQ4351646

Jan L. Cieśliński

Publication date: 16 August 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.532093

zbMATH Keywords

immersionssine-Gordon equationDarboux transformationssoliton theorypseudospherical surfacesparallel surfacesWeingarten surfacesChebyshev coordinatessurfaces in Lie algebras

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (17)

A cohomological approach to immersed submanifolds via integrable systems ⋮ Modified Korteweg–de Vries surfaces ⋮ Lax triples for integrable surfaces in three-dimensional space ⋮ Korteweg-de Vries surfaces ⋮ The Lund–Regge surface and its motion’s evolution equation ⋮ The cross ratio and Clifford algebras ⋮ Some Special Integrable Surfaces ⋮ Space-like Weingarten surfaces in the three-dimensional Minkowski space and their natural partial differential equations ⋮ On geometric aspects of the supersymmetric Fokas–Gel’fand immersion formula ⋮ The spectral interpretation of \(n\)-spaces of constant negative curvature immersed in \({\mathbb{R}}^{2n-1}\) ⋮ The motion of surfaces in geodesic coordinates and 2+1-dimensional breaking soliton equation ⋮ Deformations of surfaces associated with integrable Gauss–Mainardi–Codazzi equations ⋮ Discretization of multidimensional submanifolds associated with Spin-valued spectral problems ⋮ Surfaces and curves corresponding to the solutions generated from periodic ``seed of NLS equation ⋮ Soliton surfaces in the generalized symmetry approach ⋮ A class of linear spectral problems in Clifford algebras ⋮ A geometric interpretation of the spectral parameter for surfaces of constant mean curvature

Cites Work

• Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations
• Surfaces in Minkowski 3-space on which H and K are linearly related
• All constant mean curvature tori in \(R^ 3\), \(S^ 3\), \(H^ 3\) in terms of theta-functions
• Classically solvable field theory model
• Weingarten surfaces and nonlinear partial differential equations
• Surfaces in \(\mathbb{R}^ 3\) with prescribed curvature
• Surfaces on Lie groups, on Lie algebras, and their integrability (with an appendix by Juan Carlos Alvarez Paiva)
• An elementary geometric characterization of the integrable motions of a curve
• Isothermic surfaces in \(\mathbf E^3\) as soliton surfaces
• An effective method to compute N-fold Darboux matrix and N-soliton surfaces
• Group interpretation of the spectral parameter in the case of nonhomogeneous, nonlinear Schrödinger system
• Bäcklund transformations of linear Weingarten surfaces in Minkowski three-space
• On integrability of the inhomogeneous Heisenberg ferromagnet model: Examination of a new test
• An algebraic method to construct the Darboux matrix
• Three-dimensional distortions of a vortex filament with axial velocity

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