Search

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 ( G ′ / G) -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. [ABSTRACT FROM AUTHOR]

In this paper, we will implement a comparison between three different perceptions to the behavior of the exact solution to the generalized Hirota–Satsuma coupling Korteweg–de Vries System (GHSCKDVS). The proposed model plays a vital role in different branches of physics and applied mathematics. Specially, this model describes dispersive waves as the shallow water waves in hydrodynamics and it has various types of solutions like soliton solutions and traveling wave solutions. These three various visions to the behavior of the exact solution are established via three various techniques that have three different mathematical analyses. These three important different techniques are the Paul–Painlevé approach method (PPAM) examined previously to extract the exact solutions for many nonlinear partial differential equations (NLPDE) and achieved good results, the Ricatti–Bernolli Sub-ODE method (RBSODM) which is one of the famous ansatze approaches that doesn’t surrender to the balance rule, treats the balance rule fails and realizes impressive forms of the exact solutions. Many new various types of soliton solutions as hyperbolic and trigonometric function solutions, represented by the M-shaped, W-shaped, kink, anti-kink and dark soliton solutions have been established via these two methods. Moreover, we will document the identical numerical solutions for all achieved exact solutions realized by the two methods mentioned above via the famous numerical variational iteration method (VIM) that usually gives good results. The powerful of our achieved numerical solutions related to that their initial conditions emerged from the extracted exact solutions. [ABSTRACT FROM AUTHOR]