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

Abstract

I explore the collision of localized structures that arise from a general initial solutions in the Peyrard-Bishop model. By means of the semi-discrete approximation, it is shown that the amplitudes of waves are described by the the discrete nonlinear Schrödinger equation. The corresponding soliton solutions of this equation are obtained through the Hirota's bilinearization method. These solutions include the one-as well as the two-soliton solutions. Particular attention 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 that describes the local opening of the two strands of DNA, I show that, the enhancement of the bubbles is due to energy transfer from the pump to the bubble within the collision process. It is also shown that the underlying solitons undergo fascinating shape changing (intensity redistribution) collision.