Note on Semi-Discrete Conservation Laws and Conservation of Wave Action by Multisymplectic Runge-Kutta Box Schemes; Analysis rept

摘要

In this note we show that multisymplectic Runge-Kutta box schemes, of which the Gauss-Legendre methods are the most important, preserve a discrete conservation law of wave action. The result follows by loop integration over an ensemble of flow realizations, and the local energy-momentum conservation law for continuous variables in semi-discretizations.