Symplectic integration of PDEs using Clebsch variables (Q2323356)

This paper is focused on infinite-dimensional Lie-Poisson systems. Clebsch variables are used to lift the original system to a collective Hamiltonian system on a symplectic manifold whose symplectic structure is related to the original Lie-Poisson structure. The main example is a Burgers equation, together with some related PDEs. The authors apply symplectic integration on the resulting collective Hamiltonian systems. The numerical experiments show excellent conservation properties and indicate that the disadvantage of an increased phase-space dimension can be balanced by a proper use of symplectic integration.