Travelling waves in Hamiltonian systems on 2D lattices with nearest neighbour interactions

We study travelling waves on a two-dimensional lattice with linear and nonlinear coupling between nearest particles and a periodic nonlinear substrate potential. Such a discrete system can model molecules adsorbed on a substrate crystal surface. We show the existence of both uniform sliding states and periodic travelling waves as well in a two-dimensional sine-Gordon lattice equation using topological and variational methods.