Nonlinear dynamics of a Davydovs model with two independent excitonic modes in complex one-dimensional molecular systems

A Davydovs model of complex molecules, connected by hydrogen bonds and containing two independent excitonic modes is considered. The model nonlinearity appears only in the interaction Hamiltonian between the excitonic modes and the acoustic phonons describing the oscillations of the complex molecules along the chain. A coherent 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 averaged 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 Schroedinger 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 (authors)