A convergent finite difference scheme for the Camassa-Holm equation with general H-1 initial data

We suggest a finite difference scheme for the Camassa-Holm equation that can handle general H-1 initial data. The form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality. We prove that the difference scheme converges strongly in H-1 towards a dissipative weak solution of the Camassa-Holm equation.