https://doi.org/10.1140/epjp/s13360-023-04431-1
Regular Article
Complex Ginzburg–Landau equation in the modified Peyrard–Bishop–Dauxois model
1
Laboratory of Theoretical Physics Department of Physics, Faculty of Science, University of Bamenda, P.O. Box 39, Bambili, Cameroon
2
Laboratory of Atomic, Molecular and Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
3
African Center of Excellence in Information and Communication Technologies, University of Yaounde I, P.O. Box 8390, Yaounde, Cameroon
4
Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
5
National Advanced School of Mines and Petroleum Industries, University of Maroua, P.O. Box 46, Maroua, Cameroon
Received:
11
July
2023
Accepted:
31
August
2023
Published online:
25
September
2023
The modified Peyrard–Bishop–Dauxois model can be generalized, and through the semidiscrete approximation, we show that the dynamics of motion, associated with the DNA breather, is governed by the complex quintic Ginzburg–Landau equation. We discuss the impact of quintic term in the breather formations. The linear study of the plane wave solution has been investigated, in particular, it is shown that the instability diagram is steeply modified by the increase of the quintic parameter. One obtains wave pattern formations. Thereafter the wave patterns presented are in very robust form, which from a biological point of view, constitute opening states, observed during the vital events namely recombination-repair. These emerged structures can be strongly controlled by the quintic nonlinear parameter. The introduction of the quintic nonlinearity induces the new generations of modulated waves and also provokes the increasing of the waves amplitude. Our numerical study proves the validity of the analytical investigation where we observe the birth of wave excitations spreading with irregular features due to the increase in quintic parameter. This also confirms that the wave number falls well in the disturbance domains.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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.
