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We analyze a peakon collision for essentially non-integrable versions of the Camassa-Holm equation. Using the weak asymptotics methods, we construct a two-phase asymptotic solution that satisfies both a one-parameter family of equations and two energy laws. It is shown that the waves with initial amplitudes  when interacting, are reflected and exchange their energy: the new amplitudes will be  instead of  and  instead of  

general Camassa-Holm model, weak asymptotics, peakons, interaction, multiphasic asymptotics.