Energy-conserving Hamiltonian Boundary Value Methods for the numerical solution of the Korteweg–de Vries equation

In this paper we study the efficient solution of the well-known Korteweg–de Vries equation, equipped with periodic boundary conditions. A Fourier-Galerkin space semi-discretization at first provides a large-size Hamiltonian ODE prob- lem, whose solution in time is then carried out by means of energy-conserving methods in the HBVM class (Hamiltonian Boundary Value Methods). The effi- cient implementation of the methods for the resulting problem is also considered and several numerical examples are reported.