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. @S0163-1829~98!05133-9#