Baleanu, DumitruIbrahim, SalisuSulaiman, Tukur A.Yusuf, AbdullahiOzsahin, Dilber UzunBaleanu, Dumitru2025-05-112025-05-1120240306-89191572-817Xhttps://doi.org/10.1007/s11082-023-05571-5https://hdl.handle.net/20.500.12416/9560Ibrahim, Salisu/0000-0002-1467-5426In this paper, we examine the optical solitons for the nonlinear doubly dispersive equation and the modified Boussinesq equation, which explain the flow of shallow water in a small-amplitude surface system. We realize a variety of solitons using the Sardar sub-equation approach, including bright solitons, dark solitons, singular solitons, mixed bright-singular solitons, periodic, exponential, and rational solutions. The generated optical solutions can be used to simulate water waves and the free movement of a fluid surface, both of which are important in computing models of nonlinear partial differential equations in science, engineering, and mathematical physics. For the physical interpretation of the data, the well-known symbolic software Mathematica 12 was employed.eninfo:eu-repo/semantics/closedAccessDoubly Dispersive EquationImproved Boussinesq EquationSardar Sub-Equation MethodOptical SolitonsArticle56110.1007/s11082-023-05571-52-s2.0-85177639993WOS:001122466600040Q2Q2