Investigation of soliton dynamics and bifurcations in the fifth-order nonlinear Wazwaz equation

Abstract This study explores the significant role of soliton solutions in being stable and localized wave phenomena through diverse fields, including optical communications, fluid dynamics, and plasma physics. The investigation focuses on the fifth-order nonlinear Wazwaz equation, selected for its integrable structure and its effectiveness in modeling complex nonlinear physical processes. The modified Sardar sub-equation method is employed to obtain exact solitary wave solutions. This technique yields a wide range of analytical forms that can be written via trigonometric and hyperbolic functions. The results are shown through broad graphical analyses such as 3D, 2D, and density plots that illustrate different wave structures, including dark, lattice, periodic singular, and single solitons. In addition, a bifurcation exploration is functioned to investigate the system’s dynamic properties. Overall, this study enhances our theoretical understanding of soliton dynamics in the fifth-order Wazwaz equation and highlights its wide range of potential applications in both scientific and engineering fields.