Discussion on Peyrard Bishop DNA model for multi and breather waves, M-shaped rational and other interactional solutions

摘要

Abstract In this article, we explore analytical rational solutions to the Peyrard Bishop DNA (PB-DNA) model such as lump soliton, kink soliton, periodic cross kink, multi wave and breather lump wave. By using ansatz transformation, we explore M-shaped rational solution for PB-DNA equation. Also, we acquire M-shaped rational solution with one kink and two kink. Furthermore, we compute kink cross rational solution, homoclinic breather solution. Additionally, two forms of interactions between the kinks waves and M-shaped rational solutions will be computed. Consequently, we study the stability of the acquired solutions and present in the form of table. We also illustrate our graphs in different dimensions such as 3D, 2D, contour and stream plots.