A Hamiltonian-conserving Galerkin scheme for the Camassa–Holm equation

摘要

A new Hamiltonian-conserving Galerkin scheme for the Camassa–Holm equation is presented. The scheme has an additional welcome feature that in exact arithmetic it is unconditionally stable in the sense that the solution is always bounded. Numerical examples that confirm the theory and the effectiveness of the scheme are also given.