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Journal of Applied Nonlinear Dynamics 14(1) (2025) 53--65 | DOI:10.5890/JAND.2025.03.004

M.F. Seele$^{1}$, B. Muatjetjeja$^{1,2,3}$, T.G. Motsumi$^{1}$, A.R. Adem$^{3}$

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

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

$^{3}$ Department of Mathematical Sciences, University of South Africa, UNISA 0003, Republic of South Africa

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Abstract

In this paper, we investigate a modified (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (mAKNS) water wave equation. The method of symmetry analysis will be employed to find exact solutions of the mAKNS equation. In addition, we will implement the method of the multiplier approach to search for the admitted conserved vectors of this equation. Furthermore, a physical interpretation showing solution wave structures, density plots and wave propagation will be presented. The results obtained can be used to investigate further interaction of water waves in a variety of localized structures and high-dimensional models in other areas of nonlinear science.

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