SOLITARY WAVES OF THE VARIANT BOUSSINESQ–BURGERS EQUATION IN A FRACTAL-DIMENSIONAL SPACE

Abstract

In this work, we mainly focus on the fractal variant Boussinesq–Burgers equation which can well describe the motion of shallow water traveling along an unsmooth boundary. First, we construct its fractal variational principle and prove its strong minimum condition by the fractal Weierstrass theorem. Then two types of soliton solutions are acquired according to the constructed fractal variational principle. We find that the order of the fractal derivative hardly affects the whole shape of the solitary waves, but it remarkably affects its propagation process.