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

Area of Science:

• Nonlinear Dynamics
• Condensed Matter Physics
• Biophysics

Background:

• Proton dynamics in hydrogen-bonded networks are crucial for biological processes.
• Topological solitary waves, like kinks, can emerge in nonlinear systems.
• The double-Morse potential models complex interactions in hydrogen bonds.

Purpose of the Study:

• To investigate topological solitary waves (kinks and antikinks) in a nonlinear Klein-Gordon chain.
• To model collective proton dynamics in quasi-one-dimensional hydrogen-bonded networks.
• To analyze the stability and bifurcation of stationary kink solutions.

Main Methods:

• Utilized a nonlinear one-dimensional Klein-Gordon chain with a double-Morse on-site potential.
• Studied stationary kink solutions and their stability and bifurcation structures.
• Employed an exactly solvable model with a piecewise approximation of the double-Morse potential for analytical study.
• Investigated the Peierls-Nabarro potential and discrete traveling-wave solutions.

Main Results:

• Identified a rich variety of stationary kink solutions with different symmetry properties.
• Analyzed the stability and bifurcation structure of these kink states.
• Demonstrated the existence of discrete traveling-wave solutions.
• Established dependence of traveling waves on Morse potential anharmonicity and hydrogen bond cooperativity.

Conclusions:

• The nonlinear Klein-Gordon chain with a double-Morse potential effectively models proton dynamics in hydrogen bonds.
• The system exhibits complex kink behavior, including stable and unstable stationary states.
• Discrete traveling waves are a key feature, influenced by material properties like anharmonicity and cooperativity.