INVESTIGATION OF THE TIME FRACTIONAL GENERALIZED (2 + 1)-DIMENSIONAL ZAKHAROV–KUZNETSOV EQUATION WITH SINGLE-POWER LAW NONLINEARITY

Jian-Gen Liu, Yu-Feng Zhang and Jing-Jing Wang
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Jian-Gen Liu: School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, Jiangsu, P. R. China
Yu-Feng Zhang: School of Mathematics and Statistics, Changshu Institute of Technology, Changshu 215500, Jiangsu, P. R. China†School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China
Jing-Jing Wang: ��School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, P. R. China

FRACTALS (fractals), 2023, vol. 31, issue 05, 1-14

Abstract: In this paper, we studied the time fractional generalized (2 + 1)-dimensional Zakharov–Kuznetsov (ZK) equation with single-power law nonlinearity, which can be used to describe weakly nonlinear ion-acoustic waves in strongly magnetized lossless plasma in two dimensions. Through the fractional Lie transformation group idea, the symmetries, similarity reduction, one-parameter Lie transformation group and conservation laws of these considered equations were obtained. In addition, some new exact solutions were also constructed for them. These novel results provide a new perspective for studying the evolutionary mechanism of these considered models.

Keywords: Fractional Lie Group Scheme; Time Fractional Generalized (2 + 1)-Dimensional ZK Equation; One-Parameter Lie Group; Exact Solutions; Conservation Laws (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23500330

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