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

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 potentia...

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Bibliographic Details
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
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Summary: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).
ISSN:2331-8422
DOI:10.48550/arxiv.0208049