  A self-adaptive moving mesh method is proposed for the numerical simulations
of the Camassa-Holm equation. It is an integrable scheme in the sense that it
possesses the exact N-soliton solution. It is named a self-adaptive moving mesh
method, because the non-uniform mesh is driven and adapted automatically by the
solution. Once the non-uniform mesh is evolved, the solution is determined by
solving a tridiagonal linear system. Due to these two superior features of the
method, several test problems give very satisfactory results even if by using a
small number of grid points.
