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

• Published in: arXiv.org 2002-08
• Main Authors: Karpan, V M, Zolotaryuk, Y, Christiansen, P L, Zolotaryuk, A V
• Format: Article
• Language: English
• Subjects: Anharmonicity; Bifurcations; Chains; Dependence; Hydrogen bonding; Hydrogen bonds; Morse potential; Solitary waves; Structural stability
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0208049

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 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 travelling-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).