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Computational Solutions of Fractional (2 + 1)-Dimensional Ablowitz–Kaup–Newell–Segur Equation Using an Analytic Method and Application

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Abstract

In this paper, an efficient \((G^{\prime}/G,\,1/G)\)-expansion method is adopted to resolve a famous (2 + 1)-dimensional fractional Ablowitz–Kaup–Newell–Segur (AKNS) water wave equation for the non-conservative system that plays a significant role in understanding the wave propagation. This work addresses the physical and dynamic behavior of some new exact trigonometric, hyperbolic, and rational solitary wave solutions in the form of 3D-plots and contour plots using different measures of parameters. The obtained results show the efficiency of the proposed method for the analytical treatment of nonlinear problems in mathematics, science and engineering and may be helpful in better understanding the propagating wave dynamics in diverse situations.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, 50700, Pakistan

    Aniqa Zulfiqar & Jamshad Ahmad

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  1. Aniqa Zulfiqar
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  2. Jamshad Ahmad
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Correspondence to Jamshad Ahmad.

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Zulfiqar, A., Ahmad, J. Computational Solutions of Fractional (2 + 1)-Dimensional Ablowitz–Kaup–Newell–Segur Equation Using an Analytic Method and Application. Arab J Sci Eng 47, 1003–1017 (2022). https://doi.org/10.1007/s13369-021-05917-9

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