ON TWO-DIMENSIONAL MANIFOLDS WITH CONSTANT GAUSSIAN CURVATURE AND THEIR ASSOCIATED EQUATIONS

DOI10.1142/S0219887812500181zbMath1252.35129MaRDI QIDQ2911888

Paul Bracken

Publication date: 3 September 2012

Published in: International Journal of Geometric Methods in Modern Physics (Search for Journal in Brave)

zbMATH Keywords

integrabilitynegative curvaturesine-Gordonpositive curvaturesinh-GordonBäcklund properties

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear higher-order PDEs (35G20) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Surfaces in Euclidean and related spaces (53A05) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (1)

Geometric methods to investigate prolongation structures for differential systems with applications to integrable systems

Cites Work

• Unnamed Item
• Integrable systems of partial differential equations determined by structure equations and Lax pair
• Exterior differential systems prolongations and application to a study of two nonlinear partial differential equations
• An exterior differential system for a generalized Korteweg-de Vries equation and its associated integrability
• An analogue of Bäcklund's theorem in affine geometry
• Determination of surfaces in three-dimensional Minkowski and Euclidean spaces based on solutions of the sinh-Laplace equation
• The prolongation structures of quasi-polynomial flows
• Moving frames and prolongation algebras
• Prolongation structures of nonlinear evolution equations

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