Dynamics of Nonlinear Coherent Structures in a Hydrogen-Bonded Chain Model: The Role of the Dipole-Dipole Interactions
The problem of the energy transport along H-bonded chains has recently attracted a renewal of interest due to the close connection with basic biological processes. In our study we consider a lattice model consisting of two one-dimensional harmonically coupled sublattices corresponding to the oxygens and protons, the two sublattices being coupled. We also introduce the dipole-dipole interactions which are present as a result of the existence of microscopic dipoles created by the proton motion. This kind of interaction may affect the response of the nonlinear excitations propagating along the chain. We are looking for a solution for which the heavy-ion sublattice can be considered as “frozen”, that is the oxygens “stay” at rest and do not participate in motion. A phi-6 equation is found, which admits nonlinear excitations of solitary wave type. We have different classes of localized solutions for the proton motion and analytical expressions of these types are also given. A parallel study of the problem based on the potential is additionally presented, in a way to discuss a physical interpretation of the previous mathematical results. The proton motion is affected by the influence of the dipole interactions and the proton conductivity becomes much easier. Numerical simulations are presented for special cases. Finally, possible further extensions of the work are envisaged.
KeywordsStable Minimum Nonlinear Excitation Proton Motion Ionic Defect Basic Biological Process
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