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Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique

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  • Seadawy, Aly R.
  • Bilal, M.
  • Younis, M.
  • Rizvi, S.T.R.
  • Althobaiti, Saad
  • Makhlouf, M.M.

Abstract

In this research, we study analytically the double-chain model for deoxyribonucleic acid (DNA). The Φ6-model expansion method is used to extract the traveling wave solutions to double chain model of DNA that plays an important role in biology. The solutions obtained by this mechanism can be divided into solitary, singular, kink, single wave, combine behavior as well as a hyperbolic, plane wave, trigonometric, and the families of Jacobi solutions for elliptic functions with arbitrary parameters. The results show that the system theoretically has extremely rich exact wave structures of biological relevance.

Suggested Citation

  • Seadawy, Aly R. & Bilal, M. & Younis, M. & Rizvi, S.T.R. & Althobaiti, Saad & Makhlouf, M.M., 2021. "Analytical mathematical approaches for the double-chain model of DNA by a novel computational technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000229
    DOI: 10.1016/j.chaos.2021.110669
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    References listed on IDEAS

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    1. Sekson Sirisubtawee & Sanoe Koonprasert, 2018. "Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the -Expansion Method," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-15, June.
    2. Helal, M.A. & Seadawy, A.R. & Zekry, M.H., 2014. "Stability analysis of solitary wave solutions for the fourth-order nonlinear Boussinesq water wave equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 1094-1103.
    3. Cao, Yulei & Malomed, Boris A. & He, Jingsong, 2018. "Two (2+1)-dimensional integrable nonlocal nonlinear Schrödinger equations: Breather, rational and semi-rational solutions," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 99-107.
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    Cited by:

    1. Aly R. Seadawy & Hanadi Zahed & Syed T. R. Rizvi, 2022. "Diverse Forms of Breathers and Rogue Wave Solutions for the Complex Cubic Quintic Ginzburg Landau Equation with Intrapulse Raman Scattering," Mathematics, MDPI, vol. 10(11), pages 1-22, May.
    2. Ullah, Mohammad Safi & Baleanu, Dumitru & Ali, M. Zulfikar & Harun-Or-Roshid,, 2023. "Novel dynamics of the Zoomeron model via different analytical methods," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Rizvi, Syed T.R. & Seadawy, Aly R. & Batool, Tahira & Ashraf, M. Aamir, 2022. "Homoclinic breaters, mulitwave, periodic cross-kink and periodic cross-rational solutions for improved perturbed nonlinear Schrödinger's with quadratic-cubic nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    4. Bashir, Azhar & Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R., 2022. "The Weierstrass and Jacobi elliptic solutions along with multiwave, homoclinic breather, kink-periodic-cross rational and other solitary wave solutions to Fornberg Whitham equation," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    5. Rizvi, Syed T.R. & Seadawy, Aly R. & Raza, Umar, 2022. "Some advanced chirped pulses for generalized mixed nonlinear Schrödinger dynamical equation," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    6. Iqbal, Muhammad S. & Seadawy, Aly R. & Baber, Muhammad Z., 2022. "Demonstration of unique problems from Soliton solutions to nonlinear Selkov–Schnakenberg system," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Seadawy, Aly R. & Rizvi, Syed T.R. & Sohail, Muhammad & Ali, Kashif, 2022. "Nonlinear model under anomalous dispersion regime: Chirped periodic and solitary waves," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    8. Shami A. M. Alsallami & Syed T. R. Rizvi & Aly R. Seadawy, 2023. "Study of Stochastic–Fractional Drinfel’d–Sokolov–Wilson Equation for M-Shaped Rational, Homoclinic Breather, Periodic and Kink-Cross Rational Solutions," Mathematics, MDPI, vol. 11(6), pages 1-25, March.
    9. Akbar, Yasir & Afsar, Haleem & Abbas, Shahzad & Javed, Muhammad Waqas & Ullah, Najib, 2021. "Dromions for the coupled Maccari’s system in fluid mechanics," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    10. Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz & Bashir, Azhar, 2022. "Lump solutions, Kuznetsov–Ma breathers, rogue waves and interaction solutions for magneto electro-elastic circular rod," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    11. Seadawy, Aly R. & Rizvi, Syed T.R. & Ahmed, Sarfaraz, 2022. "Weierstrass and Jacobi elliptic, bell and kink type, lumps, Ma and Kuznetsov breathers with rogue wave solutions to the dissipative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    12. Rizvi, Syed T.R. & Seadawy, Aly R. & Farah, N. & Ahmad, S., 2022. "Application of Hirota operators for controlling soliton interactions for Bose-Einstien condensate and quintic derivative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    13. Seadawy, Aly R. & Ahmed, Sarfaraz & Rizvi, Syed T.R. & Ali, Kashif, 2022. "Lumps, breathers, interactions and rogue wave solutions for a stochastic gene evolution in double chain deoxyribonucleic acid system," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    14. Aly R. Seadawy & Syed T. R. Rizvi & Hanadi Zahed, 2023. "Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficien," Mathematics, MDPI, vol. 11(5), pages 1-16, February.

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