Modulational instability and exact soliton solutions for a twist-opening model of DNA dynamics

We study the nonlinear dynamics of DNA which takes into account the twist-opening interactions due to the helicoidal molecular geometry. The small amplitude dynamics of the model is shown to be governed by a solution of a set of coupled nonlinear Schrödinger equations. We analyze the modulational instability and solitary wave solution in the case. On the basis of this system, we present the condition for modulation instability occurrence and attention is paid to the impact of the backbone elastic constant K. It is shown that high values of K extend the instability region. Through the Jacobian elliptic function method, we derive a set of exact solutions of the twist-opening model of DNA. These solutions include, Jacobian periodic solution as well as kink and kink-bubble solitons.