Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model
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(<em>φ</em>/2)-expansion method (ITEM), t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-03-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/10.3934/math.2020163/fulltext.html |
| _version_ | 1818324225481506816 |
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| author | Jalil Manafian Onur Alp Ilhan Sizar Abid Mohammed |
| author_facet | Jalil Manafian Onur Alp Ilhan Sizar Abid Mohammed |
| author_sort | Jalil Manafian |
| collection | DOAJ |
| description | 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(<em>φ</em>/2)-expansion method (ITEM), the exp(-Ω(<em>η</em>))-expansion method (EEM), the improved exp(-Ω(<em>η</em>))-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. |
| first_indexed | 2024-12-13T11:25:12Z |
| format | Article |
| id | doaj.art-ce9ce8f36985456ca2851b9697abd277 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-13T11:25:12Z |
| publishDate | 2020-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-ce9ce8f36985456ca2851b9697abd2772022-12-21T23:48:16ZengAIMS PressAIMS Mathematics2473-69882020-03-01532461248310.3934/math.2020163Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop modelJalil Manafian0Onur Alp Ilhan1Sizar Abid Mohammed21 Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran2 Department of Mathematics, Faculty of Education, Erciyes University, 38039-Melikgazi-Kayseri, Turkey3 Department of Mathematics, College of Basic Education, University of Duhok, Zakho Street 38, 1006 AJ Duhok, IraqIn 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(<em>φ</em>/2)-expansion method (ITEM), the exp(-Ω(<em>η</em>))-expansion method (EEM), the improved exp(-Ω(<em>η</em>))-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.https://www.aimspress.com/article/10.3934/math.2020163/fulltext.htmlimproved tan(<i>φ</i>/2)-expansion methodexp(-ω(<i>η</i>))-expansion methodimproved exp(-ω(<i>η</i>))-expansion methodgeneralized (g’/g)-expansion methodthe exp-function methodsolitarytopologicalperiodic and rational solutions |
| spellingShingle | 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 AIMS Mathematics 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 |
| title | Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model |
| title_full | Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model |
| title_fullStr | Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model |
| title_full_unstemmed | Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model |
| title_short | Forming localized waves of the nonlinearity of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model |
| title_sort | forming localized waves of the nonlinearity of the dna dynamics arising in oscillator chain of peyrard bishop model |
| topic | 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 |
| url | https://www.aimspress.com/article/10.3934/math.2020163/fulltext.html |
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