Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model

Abstract

In this article, the mathematical modeling of DNA vibration dynamics has been considered that describes the nonlinear interaction between adjacent displacements along with the Hydrogen bonds with utilizing five techniques, namely, the improved tan(φ/2)-expansion method (ITEM), the exp(-Ω(η))-expansion method (EEM), the improved exp(-Ω(η))-expansion method (IEEM), the generalized (G’/G)-expansion method (GGM), and the exp-function method (EFM) to get the new exact solutions. This model of the equation is analyzed using the aforementioned schemes. The different kinds of traveling wave solutions: solitary, topological, periodic and rational, are fall out as a by-product of these schemes. Finally, the existence of the solutions for the constraint conditions is also shown.

Keywords

• improved tan(<i>φ</i>/2)-expansion method
• exp(-ω(<i>η</i>))-expansion method
• improved exp(-ω(<i>η</i>))-expansion method
• generalized (g’/g)-expansion method
• the exp-function method
• solitary
• topological
• periodic and rational solutions