Two-component solitons and their stability in hydrogen-bonded chains

The solitary-wave solutions and their stability in the case of coupled nonlinear field equations describing the proton motion in hydrogen-bonded chains are investigated. First, a model Hamiltonian for two-component solitons in hydrogen-bonded chains is proposed, and the coupled equations of motion for the two displacement fields are derived. The stationary solitary-wave solutions are found from an integral equation formulation by perturbation analysis. For the first time, a convergence proof for the fixed-point iterates of the integral equation is presented. The results show the existence of bell-shaped solitons as well as kinks in an interval of admissible soliton velocities. In the second part of the paper, the nonlinear stability of the stationary solutions is discussed. The Liapunov method is applied and a stability functional is presented. The latter yields stability conditions which are satisfied by the calculated stationary solutions. This proves the existence of stable localized finite-energy solutions in hydrogen-bonded chains which could be responsible for a very effective proton transport.