Interplay role between dipole interactions and hydrogen bonding on proton transfer dynamics

In almost all works done up to now on proton dynamics in hydrogen-bonded systems, dipole-dipole interactions have been overlooked. Here, we examine the role of these interactions on the dynamics and statistical properties of ions transfer and bonding defects in those systems. A one-dimensional model for hydrogen-bonded chains is investigated by including dipole-dipole interactions created by protons and heavy ion charge movement, generalizing thus the original Antonchenko-Davydov-Zolotaryuk model. The inclusion of dipole-dipole interactions is not only interesting from a physical point of view; it also provides an extraordinary mathematical model, a new class of differential equations possessing several key parameters and many singular straight lines. The dynamics around these singularities gives new information of great interest, such as to better explain analytically the formation of cracks resulting from dislocations observed in semiconductor heterostructures. Despite major individual differences in initial models, our results can generalize the results previously established in DNA, in the wave diffusion by static localized inhomogeneities or by generic time-dependent potentials, in nonlinear discrete electrical transmission lines and many others. Therefore, this work comes, among other things, to present a method of analytical resolution of these new equations. We use dynamic system methods to first determine the crucial parameters of the system (among them is the dipole-dipole interaction coefficient), and then we discuss on bifurcations of phase portraits and vector fields defined by the singular system. These dipole-dipole interactions have crucial effects on the response of nonlinear excitations that can propagate along these hydrogen-bonded systems. For each orbit of phase portraits with corresponding conditions, highlighting the importance of each component in the hydrogen-bonded system with dipole-dipole interactions on the dynamics, we compute all possible exact parametric representations of solutions. Our findings show that, under given parameter conditions, there are smooth solitary wave solutions, periodic wave solutions, periodic peaks, pseudo-peaks, compacton families and obviously kink and antikink solitons, specially interesting in systems with hydrogen bonds.