A convergent finite difference scheme for the Camassa–Holm equation with general H1 initial data
Giuseppe Maria Coclite, Kenneth Hvistendahl Karlsen and Nils Henrik Risebro
Abstract: We suggest a finite dfference scheme for the Camassa–Holm equation that can handle general H1 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 H1 towards an exact dissipative weak solution of Camassa–Holm equation.