Spheres, Kähler geometry and the Hunter–Saxton system

DOI10.1098/rspa.2012.0726zbMath1404.53112arXiv1108.2727OpenAlexW2962887117MaRDI QIDQ2831277

Jonatan Lenells

Publication date: 2 November 2016

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.2727

zbMATH Keywords

nonlinear partial differential equationsgeodesic flowKähler geometryshallow water wavesdiffeomorphism groups

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Geodesic flows in symplectic geometry and contact geometry (53D25)

Related Items (10)

Lie symmetry reductions and exact solutions to a generalized two-component Hunter-Saxton system ⋮ On a variation of the two-component Hunter-Saxton system ⋮ Geometric numerical integrators for Hunter-Saxton-like equations ⋮ On a two-component \(\pi \)-Camassa-Holm system ⋮ Blow-up analysis for the periodic two-component \(\mu \)-Hunter-Saxton system ⋮ Homogeneous Sobolev metric of order one on diffeomorphism groups on real line ⋮ On blow-up of solutions to the two-component \(\pi\)-Camassa-Holm system ⋮ On the global attractor of the two-component \(\pi\)-Camassa-Holm equation with viscous terms ⋮ Geometry of the Madelung transform ⋮ Geometric hydrodynamics and infinite-dimensional Newton’s equations

Cites Work

• A two-component geodesic equation on a space of constant positive curvature
• The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
• On an integrable two-component Camassa-Holm shallow water system
• On geodesic exponential maps of the Virasoro group
• On the Hunter-Saxton system
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• Euler equations on homogeneous spaces and Virasoro orbits
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• The Hunter-Saxton equation describes the geodesic flow on a sphere
• Groups of diffeomorphisms and the motion of an incompressible fluid
• The curvature of semidirect product groups associated with two-component Hunter–Saxton systems
• On the Geometry of the Kepler Problem
• Dynamics of Director Fields
• Lie Groups and Mechanics: An Introduction
• Regularization of kepler's problem and the averaging method on a manifold

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