VARIATIONAL PRINCIPLE AND SOLITARY WAVE OF THE FRACTAL FOURTH-ORDER NONLINEAR ABLOWITZ–KAUP–NEWELL–SEGUR WATER WAVE MODEL

Abstract

In this paper, for the first time in pass records, we create the fractal fourth-order nonlinear Ablowitz–Kaup–Newell–Segur (FFONAKNS) shoal water wave mold under an unsmooth boundary or in microgravity of space. With the aid of fractal traveling wave variation (FTWV) and fractal semi-inverse technology (FSIT), the fractal variational principle (FVP) is achieved, and then, using He–Weierstrass function, the strong minimum necessary condition is proved. Afterwards, the solitary wave solution is attained by FVP and minimum stationary conditions. Finally, the effect of a non-smooth border on solitary wave is deliberated and demeanors of solutions are displayed via 3D isohypse. The fractal dimension can impact the waveform, but not its apex value. The solitary wave solution (SWS) is given, and the exhibition of the technology used is not only creditable but also significant.