FRACTAL TRAVELING WAVE SOLUTIONS FOR THE FRACTAL-FRACTIONAL ABLOWITZ–KAUP–NEWELL–SEGUR MODEL

Abstract

In this paper, we mainly investigate the fractal-fractional Ablowitz–Kaup–Newell–Segur model, which is used to describe the propagation of the shallow wave water with unsmooth boundaries based on the conformable fractional derivative. A simple and powerful mathematical method is established to achieve the fractal traveling wave solutions for the fractal-fractional Ablowitz–Kaup–Newell–Segur model, which is variational reduced differential wave method. Finally, the geometric and physical properties of these fractal traveling wave solutions are elaborated by a number of three-dimensional graphics. The novel mathematical method provides a new idea for studying the fractal evolution models.