NEW PROPERTIES OF THE FRACTAL BOUSSINESQ–KADOMTSEV–PETVIASHVILI-LIKE EQUATION WITH UNSMOOTH BOUNDARIES

Abstract

The Boussinesq–Kadomtsev–Petviashvili-like model is a famous wave equation which is used to describe the shallow water waves in ocean beaches and lakes. When shallow water waves propagate in microgravity or with unsmooth boundaries, the Boussinesq–Kadomtsev–Petviashvili-like model is modified into its fractal model by the local fractional derivative (LFD). In this paper, we mainly study the fractal Boussinesq–Kadomtsev–Petviashvili-like model (FBKPLM) based on the LFD on Cantor sets. Two efficient and reliable mathematical approaches are successfully implemented to obtain the different types of fractal traveling wave solutions of the FBKPLM, which are fractal variational method (FVM) and fractal Yang wave method (FYWM). Finally, some three-dimensional (3D) simulation graphs are employed to elaborate the properties of the fractal traveling wave solutions.