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

Jalil Manafian; Onur Alp Ilhan; Sizar Abid Mohammed; Jalil Manafian; Onur Alp Ilhan; Sizar Abid Mohammed

doi:10.3934/math.2020163

AIMS Mathematics

2020, Volume 5, Issue 3: 2461-2483. doi: 10.3934/math.2020163

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Research article

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

1.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
2.
Department of Mathematics, Faculty of Education, Erciyes University, 38039-Melikgazi-Kayseri, Turkey
3.
Department of Mathematics, College of Basic Education, University of Duhok, Zakho Street 38, 1006 AJ Duhok, Iraq

Received: 28 October 2019 Accepted: 24 February 2020 Published: 09 March 2020
MSC : 65D19, 65H10, 35A20, 35A24, 35C08, 35G50

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.
Citation: Jalil Manafian, Onur Alp Ilhan, Sizar Abid Mohammed. Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model[J]. AIMS Mathematics, 2020, 5(3): 2461-2483. doi: 10.3934/math.2020163

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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.

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