Local Fractional Homotopy Perturbation Method for Solving Coupled Sine-Gordon Equations in Fractal Domain

Abstract

In this paper, the coupled local fractional sine-Gordon equations are studied in the range of local fractional derivative theory. The study of exact solutions of nonlinear coupled systems is of great significance for understanding complex physical phenomena in reality. The main method used in this paper is the local fractional homotopy perturbation method, which is used to analyze the exact traveling wave solutions of generalized nonlinear systems defined on the Cantor set in the fractal domain. The fractal wave with fractal dimension ε=ln2/ln3 is numerically simulated. Through numerical simulation, we find that the obtained solutions are of great significance to explain some practical physical problems.