  In this paper we construct a global, continuous flow of solutions to the
Camassa-Holm equation on the space H^1(R). In a previous paper [2], A. Bressan
and the author constructed spatially periodic solutions, whereas in this paper
the solutions are defined in all the real line. We introduce a distance
functional, defined in terms of an optimal transportation problem, which allows
us to study the continuous dependance w.r.t. the inital data with a certain
decay at infinity.
