Stability analysis of solutions in the helicoidal Peyrard-Bishop model of DNA molecule

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.