New Traveling Waves for DNA's Vibrational Dynamics

摘要

In this paper, we focus on studying traveling waves for the nonlinear vibrational dynamics modeling DNA, which is modified from the Yakushevich model. The Yakushevich model of DNA torsion dynamics supports soliton solutions, which are supposed to be of special interest for DNA transcription. In the discussion of the model, we will use the traveling wave and a direct integral method, in special, take the integral constant to be some special value and a special change of variable to conclude some new explicit forms of traveling waves are given including smooth solitary waves, solitary waves with blow-up points, rational solutions with decay, periodic waves and polynomial solutions. While nonlocalized ones included periodic waves and polynomial solutions. At the same time, we give the figure of the smooth solitary, solitary waves with blow-up points, rational solution with decay and periodic waves. Those obtained new waves might show some special phenomena in transporting energy.