Dynamics of exact soliton solutions in the double-chain model of deoxyribonucleic acid

In this research, we study analytically the double-chain model. The model consists of two long elastic homogeneous strands (or rods), which represent two polynucleotide chains of the deoxyribonucleic acid molecule, connected with each other by an elastic membrane (or some linear springs) representing the hydrogen bonds between the base pairs of the two chains. The new extended direct algebraic method and the generalized Kudryashov method are successfully utilized to discuss the exact soliton solutions to the double-chain model of deoxyribonucleic acid that plays an important role in biology. The solutions obtained by these mechanisms can be divided into solitary, singular, kink, single wave, combine behavior as well as hyperbolic, plane wave, and trigonometric solutions with arbitrary parameters. Some solutions have been exemplified by graphics to understand the physical meaning of the DNA model. The accomplished solutions seem with all essential constraint conditions, which are obligatory for them to subsist. Hence, our techniques via fortification of symbolic computations provide an active and potent mathematical implement for solving diverse benevolent nonlinear wave problems. The results show that the system theoretically has extremely rich exact wave structures of biological relevance.

Automated summary

This research successfully discusses the exact soliton solutions to the double-chain model of deoxyribonucleic acid using new mathematical methods, which play an important role in biology. Some solutions are exemplified graphically to understand the physical meaning of the DNA model. The results show extremely rich exact wave structures of biological relevance.