Exact travelling wave solution for the local fractional Camassa-Holm-Kadomtsev-Petviashvili equation

Abstract

In this work, the local fractional Camassa-Holm-Kadomtsev–Petviashvili equation (LFCHKPE) is defined on Cantor sets by using the local fractional derivative for the first time. The exact travelling-wave solution of the non-differential type for the LFCHKPE is obtained by using the local fractional wave method (LFWM). The LFWM is very simple and effective and then gets good results. The obtained non-differential travelling-wave solutions are elaborated by some 3D figures. A comparison with classical Camassa-Holm-Kadomtsev–Petviashvili equation (CCHKPE) is also presented. The LFWM sheds a new light on the exact travelling wave solution of local fractional wave equations.

Keywords

• Local fractional derivative
• Cantor sets
• Travelling-wave solution
• Camassa-Holm-Kadomtsev–Petviashvili equation