Stability analysis of solutions in the helicoidal Peyrard-Bishop model of DNA molecule
Anna Batova, Dragana Rankovi\'c, Slobodan Zdravkovi\'c
TL;DR
This paper analyzes the stability of kink-solitary waves in a helicoidal Peyrard-Bishop DNA model, highlighting the importance of viscosity and identifying stable subsonic solutions.
Contribution
It provides a stability analysis of kink solutions in the helicoidal Peyrard-Bishop model, emphasizing the role of viscosity in wave stability.
Findings
Supersonic kink solitons are unstable.
Subsonic kink solitons are stable.
Viscosity is essential for wave stability.
Abstract
We use the helicoidal Peyrard-Bishop model of DNA in the current work. We solve a dynamical equation of motion using a continuum approximation, resulting in kink-solitary waves that travel along the chain. We demonstrate that, whereas supersonic kink solitons are not stable, subsonic ones are. Moreover, we demonstrate the importance of viscosity by showing that no wave is stable in the absence of viscosity.
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