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Optimal solutions of Lie subalgebra, dynamical system, travelling wave solutions and conserved currents of (3+1)-dimensional generalized Zakharov–Kuznetsov equation type I

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Abstract

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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Acknowledgements

The authors appreciate the support of North-West University. This work is partially kept up by the National Nature Science Foundation of China No.11672270.

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Authors and Affiliations

  1. Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho, 2735, Republic of South Africa

    Oke Davies Adeyemo & Chaudry Masood Khalique

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong, 266590, People’s Republic of China

    Lijun Zhang

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  1. Oke Davies Adeyemo
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Correspondence to Chaudry Masood Khalique.

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Adeyemo, O.D., Zhang, L. & Khalique, C.M. Optimal solutions of Lie subalgebra, dynamical system, travelling wave solutions and conserved currents of (3+1)-dimensional generalized Zakharov–Kuznetsov equation type I. Eur. Phys. J. Plus 137, 954 (2022). https://doi.org/10.1140/epjp/s13360-022-03100-z

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