Title: Liouville integrability of conservative peakons for a modified CH equation,
Abstract: The modified Camassa-Holm equation (also called FORQ) is one of numerous
$cousins$ of the Camassa-Holm equation possessing non-smoth solitons
($peakons$) as special solutions. The peakon sector of solutions is not
uniquely defined: in one peakon sector (dissapative) the Sobolev $H^1$ norm is
not preserved, in the other sector (conservative), introduced in [2], the time
evolution of peakons leaves the $H^1$ norm invariant. In this Letter, it is
shown that the conservative peakon equations of the modified Camassa-Holm can
be given an appropriate Poisson structure relative to which the equations are
Hamiltonian and, in fact, Liouville integrable. The latter is proved directly
by exploiting the inverse spectral techniques, especially asymptotic analysis
of solutions, developed elsewhere (in [3]).