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Solitary wave solutions along with Painleve analysis for the Ablowitz–Kaup–Newell–Segur water waves equation

Syed T. R. Rizvi

Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan

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Aly R. Seadawy

Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

E-mail Address: aly742001@gmail.com

Corresponding author.

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U. Akram

Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan

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M. Younis

Department of Computer Science, University of the Punjab, Lahore, Pakistan

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, and

Ali Althobaiti

Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia

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https://doi.org/10.1142/S0217984921505485Cited by:12 (Source: Crossref)

Abstract

This study focuses on the Ablowitz–Kaup–Newell–Segur (AKNS) water waves equation. Painleve test (P-test) will be implemented to check the integrability of AKNS equation and an extended modified auxiliary equation mapping (EMAEM) architectonic is implemented to get a new set of traveling wave solutions like periodic and doubly periodic, bell type, kink, singular kink, anti-kink, trigonometric, singular, rational, combined soliton like solutions and hyperbolic solutions. Furthermore, it is analyzed that the implemented algorithm is efficient and accurate for solving nonlinear evolution equations (NLEEs). Finally, graphical simulations (2D, 3D and contours) are also provided to illustrate the detailed behavior of the solution and effectiveness of the proposed method.

Keywords:

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