A one dimensional model for hydrogen bonded chains is investigated by including the dynamical degrees of freedom of the oxygens and thus generalizing the original Antonchenko-Davydov-Zolotaryuk model. Analytical solutions are derived within a continuum approximation up to second order so that rather narrow solutions could be derived accurately enough. Numerical simulations with a set of parameters derived from infrared spectra show stable low and high speed solutions separated by a forbidden gap. There exists also an intermediate velocity range where the initial solution is unstable in the sense that it is transformed to a high speed solution with the same energy.