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In this paper, the generalized Kudryashov (GK) approach and the sine-Gordon expansion approach are used for constructing new specific analytical solutions of the deoxyribonucleic acid model, which include the well-known bell-shaped soliton, kink, singular kink, periodic soliton, contracted bell-shaped soliton and anti-bell-shaped soliton. The efficacy of these strategies demonstrates their utility and efficiency in addressing a wide range of integer and fractional-order nonlinear evolution problems. The physical relevance of the demonstrated results has been proven using three-dimensional forms. It is interesting to mention that the solutions achieved here using the provided methods are extra-extensive and may be used to explain the internal interaction of the deoxyribonucleic acid model originating in mathematical biology. The suggested approach was utilized to get exact traveling wave solutions for fractional nonlinear partial differential equations appearing in nonlinear science. [ABSTRACT FROM AUTHOR]

In this study, the improved (℘ ′ / ℘) expansion method and Exp a function method are used to construct the newly closed-form exact solutions for the deoxyribonucleic acid (DNA) model which includes hyperbolic, trigonometric and exponential solutions. These solutions include a wealth of information regarding the dynamical behavior of homogeneous long elastic rods with circular cross-sections. These rods comprise a pair of polynucleotide rods of the DNA molecule that are connected by an elastic diaphragm, demonstrating the involvement of the hydrogen bond in this communication. The performance of these approaches demonstrates their use and efficacy in solving a variety of nonlinear evolution problems of integer and fractional order. The physical significance of the established and the obtained solutions has been shown via 3D shapes. It is worth noting that the solutions obtained here via the proposed schemes are more generalized and can be helpful to demonstrate the internal interaction of the DNA model arising in mathematical biology. The proposed method has been used to obtain exact traveling wave solutions for fraction nonlinear partial differential equations (NPDEs) arising in nonlinear sciences. [ABSTRACT FROM AUTHOR]

In this paper, the double-chain model for deoxyribonucleic acid (DNA) is studied analytically by taking advantage of two reliable methodologies: the new auxiliary equation method (NAEM) and the expa function method. The deoxyribonucleic acid (DNA) contains the genetic information that creatures require for their survival and reproduction. The used approaches produce exact explicit solutions to the double chain model of DNA in mathematical biology, which are presented in this paper. Many novel solutions such as trigonometric, exponential, singular, and hyperbolic solutions, are obtained by using the aforementioned techniques. Numerical simulations are employed to supplement the obtained solutions, making this research biologically relevant. Eventually, kink wave, nonlinear wave, plane wave-front and doubly soliton profiles of solutions are presented in analysis and discussion section. It is indeed important to note that the solutions produced using these techniques are more generalized and can be more useful to demonstrate the internal interactions of the double chain DNA model. [ABSTRACT FROM AUTHOR]