Exotic radiative breather solitons in DNA-related dynamics

Umar Muhammad Dauda; Hanita Daud; Hadil Alhazmi; Nazreen Waeleh; Sani Saleh Musa; Umar Muhammad Dauda; Hanita Daud; Hadil Alhazmi; Nazreen Waeleh; Sani Saleh Musa

doi:10.3934/math.2026757

AIMS Mathematics

2026, Volume 11, Issue 6: 18614-18642. doi: 10.3934/math.2026757

Previous Article Next Article

Research article Special Issues

Exotic radiative breather solitons in DNA-related dynamics

1.
Department of Mathematics, Faculty of Computing & Mathematical Sciences, Aliko Dangote University of Science & Technology, Kano, Nigeria
2.
Department of Applied Sciences, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Malaysia
3.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
4.
Faculty of Electronics and Computer Technology and Engineering, Universiti Teknikal Malaysia Melaka (UTeM), 76100 Durian Tunggal, Melaka, Malaysia
5.
Department of Mathematics, Jigawa State College of Education & Legal Studies, Jigawa, Nigeria

Received: 18 February 2026 Revised: 10 April 2026 Accepted: 18 May 2026 Published: 24 June 2026
MSC : 35B38, 35C07, 35K57, 35L05, 35L20

We employ the variational principle of calculus and continuum approximation approach to generate a useful dynamical equations to describe the dynamics of deoxy-ribonucleic acid (DNA). Based on the choice of temperature dependent potential function, we establish a better understanding of the effect of variations in temperature $ T $ on the dynamics of the underlying system. The mathematical model yields a wave packet solution whose nonlinear superposition gives a special kind of "radiative breather soliton" possessing the periodic lossless energy transfer property. The findings show the existence of breathers in DNA dynamics and provide clear reaffirmation of solitary waves in the behaviour of DNA.
- breather solitons,
- radiative breathers,
- radiative wave packets,
- continuum approximation, modified morse potential,
- symmetric morse potential,
- dynamics,
- temperature effect
Citation: Umar Muhammad Dauda, Hanita Daud, Hadil Alhazmi, Nazreen Waeleh, Sani Saleh Musa. Exotic radiative breather solitons in DNA-related dynamics[J]. AIMS Mathematics, 2026, 11(6): 18614-18642. doi: 10.3934/math.2026757

Related Papers:

Abstract

We employ the variational principle of calculus and continuum approximation approach to generate a useful dynamical equations to describe the dynamics of deoxy-ribonucleic acid (DNA). Based on the choice of temperature dependent potential function, we establish a better understanding of the effect of variations in temperature $ T $ on the dynamics of the underlying system. The mathematical model yields a wave packet solution whose nonlinear superposition gives a special kind of "radiative breather soliton" possessing the periodic lossless energy transfer property. The findings show the existence of breathers in DNA dynamics and provide clear reaffirmation of solitary waves in the behaviour of DNA.

References

[1]	M. A. Aguero, M. De Lourdes Najera, M. Carrillo, Nonclassical solitonic structures in DNA's vibrational dynamics, Int. J. Mod. Phys. B, 22 (16), 2571–2582. https://doi.org/10.1142/S021797920803968X
[2]	R. Abazari, S. Jamshidzadeh, G. Wang, Mathematical modeling of DNA vibrational dynamics and its solitary wave solutions, Rev. Mex. Fís., 64 (2018), 590–597. https://doi.org/10.31349/revmexfis.64.590. doi: 10.31349/revmexfis.64.590
[3]	A. Chabchoub, A. Slunyaev, N. Hoffmann, F. Dias, B. Kibler, G. Genty, et al., The peregrine breather on the ZeroBackground limit as the two-soliton degenerate solution: An experimental study, Front. Phys., 9 (2021), 633549. https://doi.org/10.3389/fphy.2021.633549 doi: 10.3389/fphy.2021.633549
[4]	U. M. Dauda, M. A. Lawan, I. A. Auwal, M. M. Yusuf, On coupled time-fractional hea-equations, Bayero J. Pure Appl. Sci., 16 (2023), 53.
[5]	S. W. Englander, N. R. Kallenbach, A. J. Heeger, J. A. Krumhansl, S. Litwin, Nature of the open state in long polynucleotide double helices: Possibility of soliton excitations, Proc. Nat. Acad. Sci. USA, 77 (1980), 7222–7226. https://doi.org/10.1073/pnas.77.12.7222 doi: 10.1073/pnas.77.12.7222
[6]	E. Clementi, S. Chin, Structure and dynamics of nucleic acids, proteins, and Membranes, New York: Springer, 1986. https://doi.org/10.1007/978-1-4684-5308-9
[7]	S. M. Lindsay, Low frequency coherent vibrations of DNA: The role of the hydration shell and phosphate-phosphate interactions, In: Structure and dynamics of nucleic acids, proteins, and membranes, New York: Springer, 1986. https://doi.org/10.1007/978-1-4684-5308-9_18
[8]	K. C. Lu, E. W. Prohofsky, L. L. Van Zandt, Vibrational modes of A-DNA, B-DNA, and A-RNA backbones: An application of a green-function refinement procedure, Biopolymers, 16 (1977), 2491–506. https://doi.org/10.1002/bip.1977.360161112 doi: 10.1002/bip.1977.360161112
[9]	J. Lenhard, S. Hasse, H. Hasse, On the history of the Lennard-Jones potential, Ann. Phys., 536 (2024), 2400115. https://doi.org/10.1002/andp.202400115 doi: 10.1002/andp.202400115
[10]	J. E. Lennard-Jones, Cohesion, Proc. Phys. Soc., 43 (1931), 461. https://doi.org/10.1088/0959-5309/43/5/301 doi: 10.1088/0959-5309/43/5/301
[11]	M. Mohammad, R. Nematollah, A. Azizollah, Radiative properties of Kinks in the $sin^4(\varphi)$ system, Prog. Theor. Phys., 128 (2012), 615–627. https://doi.org/10.1143/PTP.128.615 doi: 10.1143/PTP.128.615
[12]	P. M. Morse, Diatomic molecules according to the wave mechanics, Ⅱ. Vibrational levels, Phys. Rev., 34 (1929), 57. https://doi.org/10.1103/PhysRev.34.57. doi: 10.1103/PhysRev.34.57
[13]	M. Peyrard, A. R. Bishop, Statistical mechanics of a nonlinear model for DNA denaturation, Phys. Rev. Lett., 62 (1989), 2755–2758. https://doi.org/10.1103/PhysRevLett.62.2755 doi: 10.1103/PhysRevLett.62.2755
[14]	A. J. Stone, The theory of intermolecular forces, Oxford University Press, 1996.
[15]	S. S. Sabo, U. M. Dauda, S. Babuba, A. B. Bakari, On nonlinear biharmonic dispersive wave equations, Fudma J. Sci., 9 (2025), 87–100.
[16]	S. Takeno, S. Homma, Topological solitons and modulated structure of bases in DNA double helices, Prog. Theor. Phys., 70 (1983), 308–311.
[17]	U. M. Dauda, S. S. Musa. F. K. Iyanda, Dynamics of DNA: Nonlinear interaction of solitions, Available at SSRN: 4929897, 2024.
[18]	J. D. Watson, F. H. C. Crick, A structure for deoxyribose nucleic acid, Nature, 71 (1953), 733–738.
[19]	R. M. Wartell, A. S. Benight, Thermal denaturation of DNA molecules: A copmarison of theory with experiment, Phys. Rep., 126 (1985), 67–107. https://doi.org/10.1016/0370-1573(85)90060-2 doi: 10.1016/0370-1573(85)90060-2
[20]	L. V. Yakushevich, The effect of damping, external fields and inhomogeneity on the nonlinear dynamics of biopolymers, Stud. Biophys., 121 (1987), 201–207.
[21]	L. V. Yakushevich, Nonlinear DNA dynamics: A new model, Phys. Lett. A, 136 (1989), 413–417. https://doi.org/10.1016/0375-9601(89)90425-8 doi: 10.1016/0375-9601(89)90425-8
[22]	L. V. Yakushevich, Nonlinear hysics of DNA, 2nd Edition, 2006.
[23]	L. V. Yakushevich, Nonlinear physics of DNA, John Wiley & Sons, 2004.
[24]	L. Najera, M. Carrillo, M. A. Agöuero, Non-classical solitons and the broken hydrogen bonds in DNA vibrational dynamics, Adv. Studies Theor. Phys., 4 (2010), 495–510.
[25]	V. G. Ivancevic, T. T. Ivancevic, Sine-Gordon solitons, kinks and breathers as physical models of nonlinear excitations in living cellular structures. https://arXiv.org/pdf/1305.0613

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)