Geodesic Flow and Two (Super) Component Analog of the Camassa-Holm Equation

Abstract

We derive the 2-component Camassa-Holm equation and corresponding N=1 super generalization as geodesic flows with respect to the $H^1$ metric on the extended Bott-Virasoro and superconformal groups, respectively.

arXiv commentPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Cited by in corpus (9)

• The geometry of the two-component Camassa-Holm and Degasperis-Procesi equations
• On the N=2 Supersymmetric Camassa-Holm and Hunter-Saxton Equations
• Multi-Component Integrable Systems and Invariant Curve Flows in Certain Geometries
• The Frobenius-Virasoro algebra and Euler equations
• Euler Equations Related to the Generalized Neveu-Schwarz Algebra
• Deformations of N=2 super-conformal algebra and supersymmetric two-component Camassa-Holm equation
• The two-dimensional periodic $b$-equation on the diffeomorphism group of the torus
• $G$-Strands and Peakon Collisions on $\mathrm{Diff}(\mathbb{R})$
• The two-component Camassa-Holm system in weighted $L_p$ spaces