Abstract
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.