Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2002-08-30
Nonlinear Sciences
Pattern Formation and Solitons
12 pages, 20 figures
Scientific paper
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 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).
Christiansen Peter L.
Karpan Volodymyr M.
Zolotaryuk A. V.
Zolotaryuk Yaroslav
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