ON THE GENERALIZED VARIATIONAL PRINCIPLE OF THE FRACTAL GARDNER EQUATION

Abstract

The fractal calculus has gained more widespread attention in the last years. The fractal variational principle plays a major role in the fractal travelling wave theory of the fractal PDEs. This paper develops the fractal generalized variational principle (GVP) of the fractal Gardner equation by virtue of the Semi-inverse method (SIM) for the first time. On the other hand, we also discuss and verify the fractal GVP via the fractal two-scale transform (FTST) from another dimension field. The extracted fractal GVP shows the conservation laws through the energy form in the fractal space, and can be manipulated to explore the fractal solitary wave properties.