  We show that the analytic N-soliton solution of the Camassa-Holm (CH)
shallow-water model equation converges to the nonanalytic N-peakon solution of
the dispersionless CH equation when the dispersion parameter tends to zero. To
demonstrate this, we develop a novel limiting procedure and apply it to the
parametric representation for the N-soliton solution of the CH equaiton. In the
process, we use Jacobi's formula for determinants as well as various identities
among the Hankel determinants to facilitate the asymptotic analysis. We also
provide a new representation of the N-peakon solution in terms of the Hankel
determinants.
