Travelling Waves in Hamiltonian Systems on 2D Lattices with Nearest Neighbor Interactions

摘要

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