Quantization of weakly nonlinear lattices: Envelope solitons

A method of quantizing weakly nonlinear lattices is proposed. It is based on introducing ``pseudofield'' operators. In this formalism quantum envelope solitons together with phonons are regarded as elementary quasiparticles making up a boson gas. In the classical limit the excitations corresponding to frequencies above a linear cutoff frequency are reduced to conventional envelope solitons. The approach allows one to identify a quantum soliton that is localized in space and to understand the existence of a narrow soliton frequency band.