Diverse wave solutions for the (2+1)-dimensional Zoomeron equation using the modified extended direct algebraic approach

Maheen Waqar; Khaled M. Saad; Muhammad Abbas; Miguel Vivas-Cortez; Waleed M. Hamanah; Maheen Waqar; Khaled M. Saad; Muhammad Abbas; Miguel Vivas-Cortez; Waleed M. Hamanah

doi:10.3934/math.2025578

AIMS Mathematics

2025, Volume 10, Issue 6: 12868-12887. doi: 10.3934/math.2025578

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Diverse wave solutions for the (2+1)-dimensional Zoomeron equation using the modified extended direct algebraic approach

1.
Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
2.
Department of Mathematics, College of Sciences and Arts, Najran University, Najran, Saudi Arabia
3.
Faculty of Exact, Natural and Environmental Sciences, Pontificia Universidad Católica del Ecuador, FRACTAL (Fractional Research in Analysis, Convexity and Their Applications Laboratory), Av 12 de Octubre 1076 y Roca, Apartado Quito 17-01-2184, Ecuador
4.
Applied Research Center for Metrology, Standards, and Testing, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
5.
Department of Electrical Engineering, College of Engineering and Physics, King Fahd University for Petroleum and Minerals, Dhahran, Saudi Arabia

Received: 29 March 2025 Revised: 09 May 2025 Accepted: 16 May 2025 Published: 04 June 2025
MSC : 34G20, 35A20, 35A22, 35R11

This work used the modified extended direct algebraic expansion method to find exact soliton solutions for the (2+1)-dimensional nonlinear Zoomeron equation. The modified extended direct algebraic technique employs a wave transformation and, in order to determine solutions, it then performs an algebraic expansion, compares coefficients, and balances the equation. The results were an effective acquisition of a variety of solitons with unique wave characteristics including bright, kink, periodic, singular periodic, and dark solitons. A stability investigation has confirmed the structural integrity of these solutions under minor perturbations. In the form of 2D, contour, and 3D graphical representations, the stability and propagation of these solutions were further investigated. The findings illustrate how effectively this technique can solve higher-dimensional nonlinear equations and yield more soliton solutions. Beyond broadening our knowledge of nonlinear wave behavior, this research could be beneficial in nonlinear optics, fluid motion, and plasma systems.
- modified extended direct algebraic method,
- Zoomeron equation,
- soliton,
- stability
Citation: Maheen Waqar, Khaled M. Saad, Muhammad Abbas, Miguel Vivas-Cortez, Waleed M. Hamanah. Diverse wave solutions for the (2+1)-dimensional Zoomeron equation using the modified extended direct algebraic approach[J]. AIMS Mathematics, 2025, 10(6): 12868-12887. doi: 10.3934/math.2025578

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Abstract

This work used the modified extended direct algebraic expansion method to find exact soliton solutions for the (2+1)-dimensional nonlinear Zoomeron equation. The modified extended direct algebraic technique employs a wave transformation and, in order to determine solutions, it then performs an algebraic expansion, compares coefficients, and balances the equation. The results were an effective acquisition of a variety of solitons with unique wave characteristics including bright, kink, periodic, singular periodic, and dark solitons. A stability investigation has confirmed the structural integrity of these solutions under minor perturbations. In the form of 2D, contour, and 3D graphical representations, the stability and propagation of these solutions were further investigated. The findings illustrate how effectively this technique can solve higher-dimensional nonlinear equations and yield more soliton solutions. Beyond broadening our knowledge of nonlinear wave behavior, this research could be beneficial in nonlinear optics, fluid motion, and plasma systems.

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