On a two-component $Ï$-Camassa--Holm system
arXiv:1103.3154 · doi:10.1016/j.geomphys.2012.01.001
Abstract
A novel $Ï$-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