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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.
Colin J. Cotter, Darryl D. Holm, Rossen I. Ivanov and James R. Percival, Singular solutions of cross-coupled EPDiff equations: waltzing peakons and compacton pairs; , In: BGSIAM'11 Proceedings, Eds: S. Margenov, S. Dimova and A. Slavova, Demetra Publishing, Sofia (2012), pp. 26-31.