Soliton-like excitation in a nonlinear model of DNA dynamics with viscosity - Conrad Bertrand Tabi; Alidou Mohamadou; Timoleon Crepin Kofane (Mathematical Biosciences and Engineering)
The study of solitary wave solutions is of prime significance fornonlinear physical systems. The Peyrard-Bishop model for DNA dynamics isgeneralized specifically to include the difference among bases pairs and vis-cosity. The small amplitude dynamics of the model is studied analyticallyand reduced to a discrete complex Ginzburg-Landau (DCGL) equation. Ex-act solutions of the obtained wave equation are obtained by the mean of theextended Jacobian elliptic function approach. These amplitude solutions aremade of bubble solitons. The propagation of a soliton-like excitation in a DNAis then investigated through numerical integration of the motion equations. Weshow that discreteness can drastically change the soliton shape. The impactof viscosity as well as elasticity on DNA dynamic is also presented. The profile of solitary wave structures as well as the energy which is initially evenlydistributed over the lattice are displayed for some fixed parameters.