Exact solitary wave solution for fractal shallow water wave model by He’s variational method

Abstract

In this paper, the shallow water wave with unsmooth boundaries is depicted by fractal calculus, and its exact fractal solitary wave solution is successfully found by He’s variational method. The numerical examples demonstrate that the method is simple, efficient and convenient. Finally, we elaborate the physical properties of the fractal solitary solution by some graphs. The novel scheme clears up the road to the exact fractal soliton, and it sheds a new light on the fractal soliton theory.