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.
Highlights
Nonlinear differential equations are widely used to describe various complex phenomena arising in physics, biology, chemistry, and other fields [1,2,3,4]
We mainly study the well-known (2 + 1)-dimensional Zakharov–Kuznetsov (Z-K) equation, which is first derived by Zakharov and Kuznetsov and can well describe the propagation of nonlinear ionic-sonic waves in a magnetized plasma composed of cold ions and hot isothermal electrons
Based on He’s fractal derivative, we propose the fractal (2 + 1)-dimensional Z-K
Summary
Nonlinear differential equations are widely used to describe various complex phenomena arising in physics, biology, chemistry, and other fields [1,2,3,4] The study of their solutions has always been the focus of the researchers. Have been studied by many researchers, and many effective solutions have been obtained, such as the generalized exponential rational function method [8], Lie group analysis [9], group analysis approach [10], Exp-function method [11], Coupled Burgers’ equations method [12], extended tanh method [13], and so on [14,15,16,17] These results are important and can help us study the (2 + 1)-dimensional Z-K equation.
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