EXPLORING THE FRACTIONAL WAVE PROFILES TO THE GENERALIZED TRUNCATED BOGOYAVLENSKY–KONOPELCHENKO EQUATION

This work is mainly concerned with the investigation of complex dynamic behaviors of the generalized fractional [Formula: see text] Bogoyavlensky–Konopelchenko equation, which has numerous applications in the fields of mathematical physics and fluid dynamics. This equation describes the interaction between a Riemann wave along the y-axis and a long wave along the x-axis. Additionally, this equation is implemented for the propagation of water in a liquid, stratified internal waves, shallow-water waves, and ion-acoustic waves. This study introduces novel soliton solutions to the proposed model with the use of advanced analytical methods, namely, generalized Arnous technique, generalized Riccati equation mapping method and new modified generalized exponential rational technique. We solve the proposed equation with truncated [Formula: see text]-fractional derivatives, making a substantial contribution to the existing literature. The governing equation is transformed into an ordinary differential equation by employing a suitable wave transformation with the fractional derivative, thereby achieving the desired wave structures. The wave profiles of various forms, including mixed, bright, dark, singular, complex, bright-dark, and combined solitons, are extracted. In addition, we depict 2D and 3D graphs with the appropriate parameters to demonstrate the solution’s behavior at a variety of parameter values. This investigation’s findings have the capacity to improve our comprehension of nonlinear dynamics in specific systems by demonstrating the efficacy of the methodologies implemented.