Generalized Variational Principle for the Fractal (2 + 1)-Dimensional Zakharov–Kuznetsov Equation in Quantum Magneto-Plasmas

Abstract

In this paper, we propose the fractal (2 + 1)-dimensional Zakharov–Kuznetsov equation based on He’s fractal derivative for the first time. The fractal generalized variational formulation is established by using the semi-inverse method and two-scale fractal theory. The obtained fractal variational principle is important since it not only reveals the structure of the traveling wave solutions but also helps us study the symmetric theory. The finding of this paper will contribute to the study of symmetry in the fractal space.

Keywords

• fractal variational principle
• semi-inverse method
• two-scale fractal theory
• symmetry