Abstract
The nonlinear Fokas and breaking soliton equations are important modeling equations for coastal and ocean waves, such as long water waves and tsunami waves. Moreover, these models have effective applications for simulating surface and internal waves in oceans and rivers, wave packets in finite depth water, and Riemann wave propagation interactions. By exploiting the enhanced modified simple equation approach, in this article, we have established further generic, radical, and standard solitons to the erstwhile nonlinear framework with some parameters. The reputed schematic solitons, such as bell-shaped, periodic, cuspon, compacton, plane-shaped, singular soliton, kink, and other solitons, are devised for varied scores of parameters. The accomplished results might assist in better understanding the dynamics of coastal waves modulated by the formerly acknowledged couple of nonlinear models. We have studied the impacts of physical parameters and propagation rate on wave structure and affirmed their role in changing the waveform. Three-and two-dimensional diagrams are sketched to interpret the context profiles of the obtained solitary wave solutions. The established solutions demonstrate the applicability and competence of the approach to investigating nonlinear models.