Small-amplitude envelope solitons in nonlinear lattices

The general theory of small-amplitude envelope solitons in one-dimensional lattices with cubic and quartic nonlinearities is developed. It is shown for a wide diversity of interactions among particles that the dynamics of chain excitations is governed either by the nonlinear Schr\"odinger equation or by the system of coupled nonlinear Schr\"odinger equations. In particular, the theory allows the inclusion of lattices with long-range interactions and chains with a complex cell in the unique scheme, which is the envelope function approach. Classes of solitons in diatomic lattices and in chains with long-range interactions are described as particular examples. {} 1996 The American Physical Society.