Discrete kink dynamics in hydrogen-bonded chains: the one-component model

• Published in: Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2002-12, Vol.66 (6 Pt 2), p.066603-066603
• Main Authors: Karpan, V M, Zolotaryuk, Y, Christiansen, P L, Zolotaryuk, A V
• Format: Article
• Language: English
• ISSN: 1539-3755
• DOI: 10.1103/PhysRevE.66.066603

We study topological solitary waves (kinks and antikinks) in a nonlinear one-dimensional Klein-Gordon chain with the on-site potential of a double-Morse type. This chain is used to describe the collective proton dynamics in quasi-one-dimensional networks of hydrogen bonds, where the on-site potential plays the role of the proton potential in the hydrogen bond. The system supports a rich variety of stationary kink solutions with different symmetry properties. We study the stability and bifurcation structure of all these stationary kink states. An exactly solvable model with a piecewise "parabola-constant" approximation of the double-Morse potential is suggested and studied analytically. The dependence of the Peierls-Nabarro potential on the system parameters is studied. Discrete traveling-wave solutions of a narrow permanent profile are shown to exist, depending on the anharmonicity of the Morse potential and the cooperativity of the hydrogen bond (the coupling constant of the interaction between nearest-neighbor protons).