Dispersive modified Benjamin-Bona-Mahony and Kudryashov-Sinelshchikov equations: non-topological, topological, and rogue wave solitons

Abstract

This study delves into the exploration of three distinct envelope solitons within the nonlinear dispersive modified Benjamin Bona Mahony (NDMBBM) equation, originating from seismic sea waves, and the Kudryashov-Sinelshchikov (KS) equation. The solitons emerge naturally during the derivation process, and their existence is scrutinized using the ansatz approach. The findings reveal the presence of non-topological (bright), topological (dark) solitons, and rogue wave (singular) solitons, presenting significant applications in applied research and engineering. Additionally, two-dimensional and three-dimensional revolution plots are employed with varying parameter values to scrutinize the physical characteristics of these solitons.