Fractal solitary wave solutions and variational principle of the fractal general Kadomtsev-Petviashvili equation

This work examines the fractal generalized Kadomtsev-Petviashvili equation, which describes the evolution of non-linear long waves of small amplitude. The fractal traveling wave transformation and the fractal semi-inverse method are employed to derive a fractal variational principle, which was found to be a strong minimum according to the He-Weierstrass function. The solution of the two examples is presented in the form of images. This paper demonstrates that the fractal dimension affects the waveform of the generalized Kadomtsev-Petviashvili equation.