https://doi.org/10.1140/epjb/s10051-026-01194-3
Research – Statistical and Nonlinear Physics
Nonlinear wave control in an alpha-helix proteins with an impurity: mechanisms of localization, trapping and transmission of breathers
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Pure Physics Laboratory: Group of Nonlinear Physics and Complex Systems, Department of Physics, University of Douala, P.O. Box 24157, Douala, Cameroon
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Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
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African Centre for Advanced Studies, P.O. Box 4477, Yaoundé, Cameroon
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Laboratory of Physics and Complex Systems (LaPSyC): Atomic, Radiation and Biophysics, Department of Physics and Geosciences, Faculty of Science, University of Bertoua, P.O. Box 416, Bertoua, Cameroon
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Department of Wood and Forest Sciences, Higher Institute of Agriculture, Wood, Water Resources, and Environment of Belabo, University of Bertoua, P.O. Box 416, Bertoua, Cameroon
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Botswana International University of Science and Technology, Private Mail Bag 16, Palapye, Botswana
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Received:
28
October
2025
Accepted:
26
May
2026
Published online:
29
June
2026
Abstract
This paper studies a one-stranded 
-helix of a protein chain in the presence of diagonal and off-diagonal couplings under the control of a mass impurity. Using the semi-discrete approximation and the multiple time scale method, we derive discrete and semi-discrete nonlinear Schrödinger equations. Through the phenomenon of modulational instability, the analysis of linear stability is carried out. A numerical analysis of modulational instability predicts the propagation of solitonic breather-like structures within the system under the simultaneous effect of the mass impurity and the off-diagonal coupling parameter. Furthermore, a numerical study of the impurity mode reveals that indeed the dynamics of the system is characterized by the propagation of solitary breather-like waves. Furthermore, our exploration of the interaction between the breather and the impurity mode reveals a series of physical phenomena, including trapping, reflection, and transmission. Finally, the localization associated with modulational instability in the -helix is well described, aligning analytical predictions with numerical simulations.
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© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
