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Abdel-Gawad, H. I.; Tantawy, M.; Osman, M. S.

Dynamic of DNA’s possible impact on its damage. (English) Zbl 1334.35356

Math. Methods Appl. Sci. 39, No. 2, 168-176 (2016).
Summary: In this paper, we investigate the dynamic of DNA described via DNA double-stranded model with transverse and longitudinal motions. This model admits solitary, soliton, periodic, or chirped wave solution. It is justified that the most admissible physical solution is the soliton or chirped wave solution. The stability analysis of all these solutions is performed by using the Sturm-Liouville problem and the topological invariance. We found that soliton and chirped waves are unstable so that the unbounded amplitude may occur. In the view of these models, damage of DNA membrane or bases may occur under small disturbance. Also, the suggested models will be indispensable when inhomogeneity or medium dissipation is taken into account.

Cited in 18 Documents

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D20 Protein sequences, DNA sequences
35C07 Traveling wave solutions
35C08 Soliton solutions
35B35 Stability in context of PDEs
34B24 Sturm-Liouville theory

Keywords:

the dynamic of DNA; traveling wave solutions; the unified method; stability of solutions
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References:

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