  Considered herein is the integrable two-component Camassa-Holm shallow water
system derived in the context of shallow water theory, which admits blow-up
solutions and the solitary waves interacting like solitons. Using modulation
theory, and combining the almost monotonicity of a local version of energy with
the argument on the stability of a single solitary wave, we prove that the
train of $N$ solitary waves, which are sufficiently decoupled, is orbitally
stable in the energy space $H^1(\R)\times L^2(\R)$.
