Infinite-dimensional homogeneous manifolds with translational symmetry and nonlinear partial differential equations

DOI10.1063/1.528073zbMath0644.58024OpenAlexW2017262072MaRDI QIDQ3787174

Jacek Szmigielski

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.528073

zbMATH Keywords

nonlinear partial differential equationsRiccati equationKorteweg-de Vries equationsine-Gordon equationKadomtsev-Petviashvili equationZakharov-Shabat dressing method

Mathematics Subject Classification ID

Invariance and symmetry properties for PDEs on manifolds (58J70) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

Factorization and the dressing method for the Gel'fand-Dikii hierarchy, Discretizing constant curvature surfaces via loop group factorizations: The discrete sine- and sinh-Gordon equations, Kac-Moody algebra, nonlocal symmetries, and Bäcklund transformation for KdV equation, Weighted l₁ ‐ Grassmannians and Banach Manifolds of Solutions of the KP‐ Equation and the KdV‐Equation, Non-linear partial differential equations via vector fields on homogeneous Banach manifolds

Cites Work

• Loop groups and equations of KdV type
• A nonlinear superposition principle admitted by coupled Riccati equations of the projective type
• Group theoretical approach to superposition rules for systems of Riccati equations
• Superposition principles for matrix Riccati equations
• Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles