Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis

Abstract

This article deals with studying the dynamical behavior of the DNA model proposed by Peyrard and Bishop. The proposed model is investigated using the unified method (UM). Unified method successfully extracts solutions in the form of polynomial and rational functions. The solitary wave solutions and soliton solutions are constructed. An investigation of modulation instability is also presented in this paper. 3D and 2D plots are presented to exhibit the physical behavior of some of the obtained solutions.