Solitary waves and bifurcation analysis in a double-chain DNA model

Bassant Elkalzah; Mohammed S. Ghayad; M. Y. Hamada; Hatem E. Semary; Hamdy M. Ahmed; Soliman Alkhatib; Karim K. Ahmed; Bassant Elkalzah; Mohammed S. Ghayad; M. Y. Hamada; Hatem E. Semary; Hamdy M. Ahmed; Soliman Alkhatib; Karim K. Ahmed

doi:10.3934/math.2026114

AIMS Mathematics

2026, Volume 11, Issue 1: 2852-2889. doi: 10.3934/math.2026114

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Research article

Solitary waves and bifurcation analysis in a double-chain DNA model

1.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia
2.
Department of Physics and Engineering Mathematics, Faculty of Engineering, Ain Shams University, Cairo, Egypt
3.
Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt
4.
Department of Mathematics and Engineering Physics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt
5.
College of Engineering and Technology (CET), American University in the Emirates (AUE), Dubai International Academic City, Dubai P.O. Box 503000, United Arab Emirates

Received: 25 November 2025 Revised: 15 January 2026 Accepted: 19 January 2026 Published: 28 January 2026
MSC : 35Q51, 35Q92, 37G15, 92C40

This study investigated the double-chain deoxyribonucleic acid (DNA) model that is at the heart of conservation and transmission of genetic information in biological systems. The model consists of a pair of strands that simulates DNA's intertwined chains of polynucleotides. These chains are bonded together by an elastic membrane that simulates hydrogen bonds between base pairs. To analyze the nonlinear dynamics of this system, the modified extended direct algebraic method was employed to derive exact analytical solutions, including bright solitons, dark solitons, Jacobi elliptic (JE) solutions, and periodic structures. The 3D, 2D, and polar visualizations obtained show longitudinal and transverse dynamics of the DNA helix. Visual examination of the outcomes confirmed the presence of solitary waves on DNA strands. In addition to presenting some dynamical analyses, such as bifurcation and stability analyses. The current study is a significant landmark in the area of DNA dynamics, with emphasis on prominent aspects of genetic information synthesis and transmission. The novelty of this work lies in the derivation of new exact soliton solutions to the governing DNA model that, to the best of our knowledge, have not been previously reported. The findings are expected to contribute to a deeper understanding of DNA dynamics and may also have broader implications in soliton theory, nonlinear science, plasma physics, fiber optics, and physical engineering.
- soliton solutions,
- bifurcation analysis,
- traveling wave solutions,
- Jacobi elliptic method,
- bright and dark solitons,
- DNA dynamics
Citation: Bassant Elkalzah, Mohammed S. Ghayad, M. Y. Hamada, Hatem E. Semary, Hamdy M. Ahmed, Soliman Alkhatib, Karim K. Ahmed. Solitary waves and bifurcation analysis in a double-chain DNA model[J]. AIMS Mathematics, 2026, 11(1): 2852-2889. doi: 10.3934/math.2026114

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Abstract

This study investigated the double-chain deoxyribonucleic acid (DNA) model that is at the heart of conservation and transmission of genetic information in biological systems. The model consists of a pair of strands that simulates DNA's intertwined chains of polynucleotides. These chains are bonded together by an elastic membrane that simulates hydrogen bonds between base pairs. To analyze the nonlinear dynamics of this system, the modified extended direct algebraic method was employed to derive exact analytical solutions, including bright solitons, dark solitons, Jacobi elliptic (JE) solutions, and periodic structures. The 3D, 2D, and polar visualizations obtained show longitudinal and transverse dynamics of the DNA helix. Visual examination of the outcomes confirmed the presence of solitary waves on DNA strands. In addition to presenting some dynamical analyses, such as bifurcation and stability analyses. The current study is a significant landmark in the area of DNA dynamics, with emphasis on prominent aspects of genetic information synthesis and transmission. The novelty of this work lies in the derivation of new exact soliton solutions to the governing DNA model that, to the best of our knowledge, have not been previously reported. The findings are expected to contribute to a deeper understanding of DNA dynamics and may also have broader implications in soliton theory, nonlinear science, plasma physics, fiber optics, and physical engineering.

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