Least Action Principle for an Integrable Shallow Water Equation

DOI10.2991/jnmp.2001.8.4.3zbMath0992.35088arXivmath-ph/0209053OpenAlexW2115851290MaRDI QIDQ2766059

Boris Kolev, Adrian Constantin

Publication date: 24 January 2002

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

Full work available at URL: https://arxiv.org/abs/math-ph/0209053

zbMATH Keywords

Riemannian geometrygeodesicsCamassa-Holm equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (5)

A numerical study of variational discretizations of the Camassa-Holm equation ⋮ Multi-symplectic integration of the Camassa-Holm equation ⋮ Lie Groups and Mechanics: An Introduction ⋮ Hk Metrics on the Diffeomorphism Group of the Circle ⋮ A semi-discrete scheme derived from variational principles for global conservative solutions of a Camassa–Holm system

Cites Work

• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• A shallow water equation as a geodesic flow on the Bott-Virasoro group
• On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Groups of diffeomorphisms and the motion of an incompressible fluid
• A shallow water equation on the circle
• An integrable shallow water equation with peaked solitons

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