Uniqueness of Conservative Solutions to the Camassa-Holm Equation via Characteristics

The paper provides a direct proof the uniqueness of solutions to the Camassa-Holm equation, based on characteristics. Given a conservative solution u = u(t,x), an equation is introduced which singles out a unique characteristic curve through each initial point. By studying the evolution of the quantities u and v = 2arctanux along each characteristic, it is proved that the Cauchy problem with general initial data u0 ∈ H 1 (IR) has a unique solution, globally in time.