New traveling wave solutions for the extended (3+1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff and the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave equations using efficient techniques

This study develops novel solitary wave solutions for the recently introduced extended (3+1)-dimensional KdV-Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation and the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur (AKNS) water wave equation with a perturbation parameter. We employ the improved generalized Riccati equation method on the KdV-CBS equation and the generalized Kudryashov method on the AKNS equation to derive fascinating and robust wave solutions, including hyperbolic, trigonometric, and rational exponential functions. Maple software is utilized to manage the complex symbolic computations involved in these methods. The results demonstrate that the derived solutions are more general and effective than those found in existing literature, offering a broader range of solutions compared to previous methodologies. Furthermore, selected solutions are visualized to elucidate various nonlinear wave phenomena, including kink, breather, dark, and bright waves. These findings provide significant insights into the dynamics of water waves, fluid dynamics, plasma physics, and oceanography.