Conservative Finite Difference Schemes for the Degasperis-Procesi Equation(Theory)

Abstract

We consider the Degasperis-Procesi equation, which was recently introduced as a completely integrable shallow water equation. We propose nonlinear and linear finite difference schemes for the equation based on an extended version of the discrete variational derivative method, and show that they preserve two associated invariants at a same time. We also prove the unique solvability of the schemes, and evaluate the schemes numerically.