On a two-component $\pi$-Camassa--Holm system

Abstract

A novel $\pi$-Camassa--Holm system is studied as a geodesic flow on a semidirect product obtained from the diffeomorphism group of the circle. We present the corresponding details of the geometric formalism for metric Euler equations on infinite-dimensional Lie groups and compare our results to what has already been obtained for the usual two-component Camassa--Holm equation. Our approach results in well-posedness theorems and explicit computations of the sectional curvature.

12 pages

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Cited by in corpus (1)

• A note on multi-dimensional Camassa-Holm type systems on the torus