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Solitary waves solutions and local conserved vectors for extended quantum Zakharov–Kuznetsov equation

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Abstract

This paper studies a \((3+1)\)-dimensions extended quantum Zakharov–Kuznetsov (qZK) equation. The quantum Zakharov–Kuznetsov (qZK) equation models several physical phenomena such as ion-acoustic waves in a magnetized plasma composed of cold ions and hot isothermal electrons. The quantum plasmas and their new structures have attracted researchers at both experimental and theoretical level. The powerfulness of this equation resulted in many scholars finding closed-form solutions of this equation so as to have exhaustive understanding of certain physical features embedded in the qZK equation. Soliton solutions have become one of the most significant solutions in solving nonlinear evolution equations (NLEEs) due to their applications in different physical fields like plasma physics, solid state physics, neural physics and diffusion process. With this reason, we aim to implement ansatz methods to derive a variety of soliton solutions such as bright, singular and dark solitary waves solutions. Furthermore, we will construct local conservation laws via the variational approach. Thereafter, the dynamical behaviors through graphical representation of the derived solutions will be discussed in detail.

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Acknowledgements

I. Humbu would like to thank University of Botswana (UB) for their financial support.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Botswana, Private Bag 22, Gaborone, Botswana

    I. Humbu, B. Muatjetjeja & T. G. Motsumi

  2. Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X2046, Mmabatho, 2735, Republic of South Africa

    B. Muatjetjeja

  3. Department of Mathematical Sciences, University of South Africa, UNISA, Pretoria, 0003, Republic of South Africa

    A. R. Adem

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  1. I. Humbu
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Correspondence to B. Muatjetjeja.

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Humbu, I., Muatjetjeja, B., Motsumi, T.G. et al. Solitary waves solutions and local conserved vectors for extended quantum Zakharov–Kuznetsov equation. Eur. Phys. J. Plus 138, 873 (2023). https://doi.org/10.1140/epjp/s13360-023-04470-8

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