Solitary wave solutions and multistability analysis of the $(1+1)$-D Estevez-Mansfield-Clarkson model

This study investigates nonlinear evolution equations by taking the \\((1+1)\\) -D Estevez-Mansfield-Clarkson model (EMCM) as a representative model, which characterizes the complex dynamics of shallow water waves alongside the physics governing fluids. Through the application of the generalized logistic equation approach and the generalized Arnous’s technique, exact analytical solutions and the dynamics of solitons related to the \\((1+1)\\) -D EMCM are derived. We developed a diverse class of wave solutions, including dark soliton solutions, kink soliton solutions, lump soliton solutions, and periodic wave solutions. By assigning suitable values to the parameters, the dynamic characteristics of the developed wave solutions are depicted graphically using 3 D surface density graphs, line plots, and contour plots. These solutions appear to be new, as they have not been documented in any prior research. Additionally, by adjusting the initial conditions, we explore multistability analysis, which illustrates the system’s potential to present various stable states based on the choice of appropriate parametric values. Simultaneously, this study makes a significant and novel contribution to the analysis of the system, enhancing our understanding of localized waves and the dynamics of nonlinear wave phenomena in fluid systems.