Abstract
Shallow water waves are one of the most prominent and widely used waves in coastal areas. The anomalous bi-directional transmission of long waves over shallow water is described by the nonlinear fractional partial differential equations (NLFPDEs), namely space-time-fractional coupled Whitham-Broer-Kaup (WBK) and coupled approximate long water (ALW) wave equations. To achieve new analytical solutions, the enhanced extended tanh-function technique for the mentioned fractional equations in the sense of conformable derivative is used. Some well-known wave shapes of solitons, namely, kink, bell-shape, and other types, through the suggested technique are achieved, and the 3D, contour, list point plots, and vector plots of the solutions are sketched to further illustrate the wave profile. The results achieved in this study have been validated using the computational software Maple and found to be accurate. It is observed that the method is realistic, and dependable to investigate more generalized analytical wave solutions.
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