Multiple states of intrinsic localized modes

In the framework of the continuum approximation, localized modes in nonlinear lattices ("intrinsic localized modes" or "discrete breathers") are described by the nonlinear Schrödinger (NLS) equation. We go beyond this approximation and analyze what kind of qualitatively new effects can be introduced by discreteness. Taking into account the higher-order linear and nonlinear dispersion terms in the NLS equation derived from a lattice model, we predict the existence of bound states of intrinsic localized excitations. These bound states of nonlinear localized modes are also found numerically for a discrete chain with linear and nonlinear cubic interparticle interaction.