Abstract
In this paper, for the first time, the fractal–fractional short water wave model (FFSWWM) is used to simulate the propagation of seawater waves with unsmooth boundaries or in microgravity, where the conformable fractional derivative sense is adopted. A new and simple approach is presented to derive a variety of fractal solitary wave solutions of FFSWWM, which is called the sech function wave method. These obtained fractal solitary wave solutions are completely new and different from the existing literature. The fractal dynamical behavior of the gained fractal solitary wave solutions is presented by sketching some 2D and 3D graphics with different fractal dimensions and fractal parameters, which are very helpful for further study of the propagation of complex ocean waves.
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