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We introduce EPDiff equations as Euler-Poincare´ equations related to Lagrangian provided by a metric, invariant under the Lie Group Diff(Rn). Then we proceed with a particular form of EPDiff equations, a cross coupled two-component system of Camassa-Holm type. The system has a new type of peakon solutions, 'waltzing' peakons and compacton pairs.
Cotter, C.J., Holm, D.D. & Ivanov, R.I. (2012). Singular Solutions of Coss-coupled EPDiff Equations: Waltzing Peakons and Compacton Pairs. BGSIAM'11 Proceedings, Sofia (2012), pg. 26-31. doi:10.21427/r7rn-r265