The analysis of operator splitting methods for the Camassa-Holm equation

In this paper, the convergence analysis of operator splitting methods for the Camassa-Holm equation is provided. The analysis is built upon the regularity of the Camassa-Holm equation and the divided equations. It is proved that the solution of the Camassa-Holm equation satisfies the locally Lipschitz condition in H1 and H2 norm, which ensures the regularity of the numerical solution. Through the calculus of Lie derivatives, we show that the Lie-Trotter and Strang splitting converge with the expected rate under suitable assumptions. Numerical experiments are presented to illustrate the theoretical result.