Optimal solutions of Lie subalgebra, dynamical system, travelling wave solutions and conserved currents of (3+1)-dimensional generalized Zakharov–Kuznetsov equation type I
Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Private Bag X 2046, Mafikeng Campus, 2735, Mmabatho, Republic of South Africa
2 College of Mathematics and Systems Science, Shandong University of Science and Technology, 266590, Qingdao, Shandong, People’s Republic of China
Accepted: 1 July 2022
Published online: 24 August 2022
In this paper, we analytically examine a (3+1)-dimensional generalized Zakharov–Kuznetsov equation which contains the (3+1)-dimensional ZK as well as mKdV–ZK equations. We contemplate both the power-law and dual power-law of the equation. We subsequently utilize the Lie symmetries technique to reduce the partial differential equations to various ordinary differential equations via an optimal system of Lie subalgebras in one dimension. Furthermore, diverse travelling wave solutions are obtained. These solutions include various kinds of solitary wave solutions, periodic wave solutions as well as two families of unbounded exact solutions. In order to appreciate the somatic appearance of this model, we pictorially depict the motions of the secured results. Imposing the Helmholtz conditions, we gain the conserved vectors by engaging Noether’s theorem.
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