Soliton patterns and breakup thresholds in hydrogen-bonded chains

The dynamics of protons in hydrogen-bonded quasi one-dimensional networks are studied using a diatomic lattice model of protons and heavy ions including a φ 4 on-site substrate potential. It is shows that the model with linear and nonlinear coupling of the quartic type between lattice sites for the protons admits a richer dynamics that cannot be produced with linear couplings alone. Depending on two types of physical boundary conditions, namely of the drop or condensate type, and on conditions requiring the presence of linear and nonlinear dispersion terms, soliton patterns of compact support, whether with a peak, drop, bell, cusp, shock, kink, bubble or loop structure, are obtained within a continuum approximation. Phase trajectories as well as analytical studies provide information on the disintegration of soliton patterns upon reaching some critical values of the lattice parameters. The total energies of soliton patterns are computed exactly in the continuum limit. We also show that when anharmonic interactions of the phonon are taken into account, the width and energy of soliton patterns are in qualitative agreement with experimental data. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007