On a two-component $π$-Camassa--Holm system

Details On a two-component $π$-Camassa--Holm system On a two-component $π$-Camassa--Holm system

2011-03-16

arxiv.org/abs/1103.3154v3

J. Geom. Phys. 62 (2012) 832-838

Mathematics

Analysis of PDEs

12 pages

Scientific paper

10.1016/j.geomphys.2012.01.001

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.

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