Analysis of soliton phenomena in (2+1)-dimensional Nizhnik-Novikov-Veselov model via a modified analytical technique

Saima Noor; Azzh Saad Alshehry; Asfandyar Khan; Imran Khan; Saima Noor; Azzh Saad Alshehry; Asfandyar Khan; Imran Khan

doi:10.3934/math.20231439

AIMS Mathematics

2023, Volume 8, Issue 11: 28120-28142. doi: 10.3934/math.20231439

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Analysis of soliton phenomena in (2+1)-dimensional Nizhnik-Novikov-Veselov model via a modified analytical technique

1.
Department of Basic Sciences, Preparatory Year Deanship, King Faisal University, Al-Ahsa, 31982, Saudi Arabia
2.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
3.
Department of Mathematics, Abdul Wali Khan University Mardan, Pakistan
4.
Department of Mathematics and Statistics, Bacha Khan University Charsadda 24420, Pakistan

Received: 20 August 2023 Revised: 22 September 2023 Accepted: 02 October 2023 Published: 12 October 2023
MSC : 33B15, 34A34, 35A20, 44A10, 35A22

The present research applies an improved version of the modified Extended Direct Algebraic Method (mEDAM) called $ r $+mEDAM to examine soliton phenomena in a notable mathematical model, namely the (2+1)-dimensional Nizhnik-Novikov-Veselov Model (NNVM), which possesses potential applications in exponentially localized structure interactions. The generalized hyperbolic and trigonometric functions are used to disclose a variety of soliton solutions, including kinks, anti-kink, bell-shaped and periodic soliton. Some 3D graphs are plotted for visual representations of these solutions which highlight their adaptability. The results provide a basis for practical usage and expansions to related mathematical models or physical systems. They also expand our understanding of the NNVM's dynamics, providing insights into its behavior and prospective applications.
- partial differential equations,
- Nizhnik-Novikov-Veselov model,
- modified extended direct algebraic method,
- variable transformation,
- soliton,
- incompressible fluid,
- shallow water wave
Citation: Saima Noor, Azzh Saad Alshehry, Asfandyar Khan, Imran Khan. Analysis of soliton phenomena in (2+1)-dimensional Nizhnik-Novikov-Veselov model via a modified analytical technique[J]. AIMS Mathematics, 2023, 8(11): 28120-28142. doi: 10.3934/math.20231439

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Abstract

The present research applies an improved version of the modified Extended Direct Algebraic Method (mEDAM) called $ r $+mEDAM to examine soliton phenomena in a notable mathematical model, namely the (2+1)-dimensional Nizhnik-Novikov-Veselov Model (NNVM), which possesses potential applications in exponentially localized structure interactions. The generalized hyperbolic and trigonometric functions are used to disclose a variety of soliton solutions, including kinks, anti-kink, bell-shaped and periodic soliton. Some 3D graphs are plotted for visual representations of these solutions which highlight their adaptability. The results provide a basis for practical usage and expansions to related mathematical models or physical systems. They also expand our understanding of the NNVM's dynamics, providing insights into its behavior and prospective applications.

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