Extended Jacobian Elliptic Function Expansion Method and Its Applications in Biology

Abstract

In this work, an extended Jacobian elliptic function expansion method is proposed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to Dynamical system in a new Double-Chain Model of DNA and a diffusive predator-prey system which play an important role in biology.

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

“…The solitonic structures obtained in this study could attract the attention of researchers working in the field of biology. The comparison of our results with the outcomes of previous works [35][36][37][38][39][40][41][42][43] shows that kink and combo solitons as well as multiple soliton, singular soliton, and singular periodic soliton solutions have been found for the first time in this article. Moreover, these results have some other physical meanings; for instance, the hyperbolic tangent arises in the calculation of magnetic moment and rapidity of special relativity, the hyperbolic secant arises in the profile of a laminar jet, and hyperbolic cotangent arises in the Langevin function for magnetic polarization.…”

“…To have the clear and good understanding, physical behavior of some reported solutions has been exhibited through 3D and 2D graphs under the suitable values of parameters. The graphical representation of kink, singular, and periodic wave solutions which appear in Equations (28,29,78,79), (36,37), and (42,43) can be seen in Figures 1-8, respectively. Hence, we conclude that our present mathematical methods could be fruitful tools in the applied science.…”

“…Nonlinearity has been shown to be responsible to create localized waves. These localized waves are interesting because they have the capability to transport energy without dissipation 35–43 . References 35–37 indicate that a new model with a double chain of DNA is made up of two long, elastic, and homogeneous strands that represent two polynucleotide chains of DNA molecule linked by an elastic membrane which represents the hydrogen bonds between the base pair of two chains.…”

“…These localized waves are interesting because they have the capability to transport energy without dissipation. [35][36][37][38][39][40][41][42][43] References [35][36][37] indicate that a new model with a double chain of DNA is made up of two long, elastic, and homogeneous strands that represent two polynucleotide chains of DNA molecule linked by an elastic membrane which represents the hydrogen bonds between the base pair of two chains. In this work, we have applied two analytical mathematical methods for developing the exact soliton solutions of the DNA system that play an important role in biological related studies.…”

“…Under reasonable approximation, the new double-chain model of DNA can be described by the following two general nonlinear dynamical system. [35][36][37] 𝜙 tt − 𝛼 2 1…”