Effective Hamiltonian for traveling discrete breathers in the FPU chain

For the Fermi-Pasta-Ulam chain, an effective Hamiltonian is constructed, describing the motion of approximate, weakly localized discrete breathers traveling along the chain. The velocity of these moving and localized vibrations can be estimated analytically as the group velocity of the corresponding wave packet. The Peierls-Nabarro barrier is estimated for strongly localized discrete breathers.