Soliton-like Solution on the Dynamics of Modified Peyrard-Bishop DNA Model in the Thermostat as a Bio-Fluid

The Peyrard-Bishop (PB) DNA model is the most representative model to investigate DNA dynamics because the model is able to answer DNA denaturation processes even though the model has restricted review that DNA assumes without surrounding interaction. In this study, we investigate the dynamics of the modified PB DNA model by considering DNA in the Nosé-Hoover thermostat as a bio-fluid with various viscosities. Viscosity variations are reviewed through temperature variations, namely thermal viscosity. We attain the dynamical equation of DNA in the form of a nonlinear Schrödinger-like (NLS-like) equation by using the perturbation method and continuous approximation. We solve the NLS-like equations by the numerical split-step Fourier method. We obtain a soliton-like solution for the dynamics of this specific DNA model. The behavior of the soliton-like solution fluctuates as the temperature increases, representing the fluctuational openings of DNA, i.e., denaturation bubbles. In addition, that behavior also evolves with variations of the perturbation parameter. Moreover, we obtain soliton-like solutions by balancing the perturbation and the nonlinearity of the DNA system from the bio-fluid interaction. Furthermore, for the specific thermal viscosity of bio-fluid, we gain the denaturation temperature at 370 K ≤ T ≤ 380 K.