Formation and Interaction of Bright Solitons with Shape Changing in a DNA Model

Abstract

I explore the collision of localized structures that arise from ageneral initial solutions in the Peyrard- Bishop model. By meansof the semi-discrete approximation, it is shown that the amplitudesof waves are described by the the discrete nonlinear Schr�dingerequation. The corresponding soliton solutions of this equation areobtained through the Hirota�s bilinearization method. These solutionsinclude the one- as well as the two-soliton solutions. Particularattention is paid to the behaviors displayed by the two-soliton solution.Taking one of the soliton as a pump and the other as the bubble thatdescribes the local opening of the two strands of DNA, I show that,the enhancement of the bubbles is due to energy transfer from thepump to the bubble within the collision process. It is also shownthat the underlying solitons undergo fascinating shape changing (intensityredistribution) collision.