NUMERICAL INVESTIGATION OF NONLINEAR DISPERSIVE WAVE STRUCTURES IN THEROSENAU – HYMAN AND GILSON–PICKERING EQUATIONS - Adebisi, Ajimot F.; Kolawole, Mutairu K.; Babalola, Olutola O. (FUDMA Journal of Sciences, 2025)
This paper investigates the nonlinear Gilson–Pickering equation, a model unifying several key dispersive equations. We employ to derive a new numerical approach and diverse family of exact traveling wave solutions. These solutions include bright solitons, dark solitons, singular solitons, and periodic solutions, which generalize and extend previously known results(Akgül et al., 2020, Ak et al., 2016& Barretta et al., 2004).The physical characteristics of the obtained solutions are analyzed graphically, providing insight into the wave dynamics governed by the equation. Our results confirm the efficacy of the chosen method and enrich the set of analytical solutions available for this important class of nonlinear evolutionary equations.
Keywords: Rosenau–Hyman equation; Gilson–Pickering equation; nonlinear dispersion; soliton; compacton; spectral collocation method; numerical analysis