Soliton Dynamics in Combined KdV-mKdV and KdV-nKdV Models: A Riccati-Bernoulli Sub ODE Approach - Jibrin Sale Yusuf; Umar Sani Muhammad (Vokasi UNESA Bulletin of Engineering, Technology and Applied Science, 2026)
We investigate new soliton solutions of two coupled nonlinear systems: the combined KdV–nKdV and the KdV–mKdV equations. Using the Riccati–Bernoulli Sub-ODE (RBSODE) method with r = 0, the models are reduced to tractable algebraic forms that yield explicit trigonometric, hyperbolic, and exponential-type soliton families. The analytical procedure reveals parameter conditions under which compressive and oscillatory solitons emerge, such as δ/α2(α+δ)>0 for localized bright solitons. A systematic parameter study quantifies how amplitude, width, and velocity vary with the nonlinear coefficients α, δ, p, q. Comparison with existing results (Wazwaz 2017) shows that our solutions recover known families as special cases while extending them to additional parameter regimes. Physical implications are discussed in the context of nonlinear wave propagation in dispersive media, where the balance between quadratic and cubic nonlinearities governs soliton shape and robustness. The results demonstrate that the RBSODE approach provides a flexible symbolic framework for constructing diverse soliton families and analyzing their parameter dependence in coupled nonlinear systems.