One-dimensional lattice dynamics of hydrogen bonded systems

A one-dimensional continuum model of a hydrogen bonded system is considered. The model takes into account the interaction of the proton displacements with the deformation of the lattice of heavy ions. The existence is established of two soliton (slow and fast) and two phonon (low- and high-frequency) modes, for which the ranges of the protonsubsystem-lattice coupling constants and also the velocity intervals are determined. By the introduction of a dynamical collective variable that determines the soliton position the equations of motion of the system can be represented in the form of a dynamical equation for a particle.