A FRACTAL MODIFICATION OF THE SHARMA-TASSO-OLVER EQUATION AND ITS FRACTAL GENERALIZED VARIATIONAL PRINCIPLE

The Sharma-Tasso-Olver equation can well describe the wave motion in physics, however, it becomes ineffective when the boundary is non-smooth, so a modification of the equation is urgently needed. In this study, we derive a new fractal Sharma-Tasso-Olver equation that can model the wave motion with the non-smooth boundary by applying He's fractal derivative. By means of the semi-inverse method, we successfully establish its fractal generalized variational principle, which provides the conservation laws in an energy form in the fractal space and reveals the possible solution structures of the equation. The obtained generalized variational principle can be used for the numerical and analytical studies of the solitary wave properties in the fractal PDEs.