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 Schrodinger 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.
Highlights
DNA dynamics continues to attract a great deals of interest nowadays
The interest in the nonlinear dynamics of DNA started when Englander et al [1] suggested that the existence of solitons propagating along the DNA molecule may be important in a process called “DNA transcription”
There are two important models, the one proposed by Yakushevich [2] and improved by Gaeta [3], and the second proposed by Peyrard and Bishop (PB) [4] which concentrate on transversal openings of base pairs
Summary
DNA dynamics continues to attract a great deals of interest nowadays. Its complex structure and dynamical features are on the basis of life at the molecular level. The model has been successfully applied to analyze experiments on the melting of short DNA chains [5] It allows to include the effect of heterogeneities [6] yielding a sharp staircase structure of the melting curve (number of open base pairs as a function of the temperature T) [7]. The nonlinear effects might focus the vibration energy of DNA into localized soliton-like excitations [10,11,12,13,14,15]. In section“model and mathematical background”, after a brief presentation of the PB model of DNA dynamics, I sketch the discrete expansion method that allows me to obtain the equation that governs the amplitude of planar waves in the form of the DNLS equation. It is convenient to think about reducing equation 7 to a more simple system that, under some approximations, can allow us to find
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
