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