Nonlinear Dynamics of a Davydov’s Model with Two Independent Excitonic Modes in Complex One-Dimensional Molecular Systems

摘要

A Davydov's model of complex molecules, connected by hydrogen bonds and containing two independent excitonic modes is considered. The model nonlinearity ap- pears only in the interaction Hamiltonian between the excitonic modes and the acoustic phonons describing the oscillations of the complex molecules along the chain. A coher- ent state is used to describe the extended localized states and the equations of motion for the classical exciton amplitudes and the phonon field are obtained from the aver- aged Hamiltonian. In a multiple scales analysis the discrete equations are reduced to a coupled system of differential equations for the first order excitonic amplitudes and the phonon field. In the non-resonant case the problem is characterized by a system of coupled nonlinear Schr" odinger equations for the excitonic amplitudes. In the resonant case (long wave – short wave resonance) a two component Yajima-Oikawa system is obtained and the one-soliton solution is explicitly presented.