Dynamics of Soliton Collision in DNA Double Helix

Abstract

The presence of solitary wave excitation in biopolymers offers a framework for understanding processes such as energy transport, localization, transcription, and translation. While numerous models have been proposed to explain these biomolecular processes, we consider the helicoidal Peyrard-Bishop (HPB) model, incorporating the combined effects of viscosity and solvent interaction. By applying a semidiscrete approximation to the obtained Hamiltonian and performing further transformations, we derive a nonlinear Schrödinger equation with a perturbation term that depends on the solvent interaction potential. Using the Hirota bilinearization method, we obtain one- and two-soliton solutions. Analysis of the collision profiles reveals inelastic interactions, resulting in an uneven exchange of energy between the solitary waves. This uneven energy exchange leads to the suppression of one of the solitary waves.