New variety diverse solitary wave solutions to the DNA Peyrard–Bishop model

In this study, we will derive many new diverse performances for the solitary wave solutions to the DNA Peyrard–Bishop Model with Beta-Derivative (DNAPBM) via three distinctive techniques. The first one has profile name: The ([Formula: see text]/[Formula: see text]-expansion method, while the second one has the profile name: the extended direct algebraic method (EDAM) and the third one has the profile name: the Paul-Painlevé approach method (PPAM). The three techniques are implemented in the same vein and are parallel. The agreement between the achieved solitary wave solutions by these suggested three techniques has been shown. The novelty of our results will appear when the comparison is implemented between our obtained solutions and that achieved previously by other authors who applied another technique.