Title: Numerical solutions of Hamiltonian PDEs: a multi-symplectic integrator in light-cone coordinates,
Abstract: We introduce a novel numerical method to integrate partial differential
equations representing the Hamiltonian dynamics of field theories. It is a
multi-symplectic integrator that locally conserves the stress-energy tensor
with an excellent precision over very long periods. Its major advantage is that
it is extremely simple (it is basically a centered box scheme) while remaining
locally well defined. We put it to the test in the case of the non-linear wave
equation (with quartic potential) in one spatial dimension, and we explain how
to implement it in higher dimensions. A formal geometric presentation of the
multi-symplectic structure is also given as well as a technical trick allowing
to solve the degeneracy problem that potentially accompanies the
multi-symplectic structure.