Nonlinear surface modes in monoatomic and diatomic lattices

We investigate the structure and stability of nonlinear surface modes in one-dimensional monoatomic and diatomic lattices. For a monoatomic lattice, we show analytically and numerically that nonlinearity can support a stable surface mode whose maximum amplitude is shifted from the surface. In the limit of strong nonlinearity when this mode is localized on a few atoms near the surface, we find the surface mode's structure for a wide range of the mass ratio parameter and reveal multistability of the localized modes. For diatomic lattices, we use the quasi-continuum approximation to describe analytically nonlinear surface gap modes comparing our results with recent numerical simulations. We show that even weak nonlinearlity can dramatically change the region of existence of surface modes in discrete lattices.