Solitary wave solutions to Gardner equation using improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method

Ghazala Akram; Maasoomah Sadaf; Mirfa Dawood; Muhammad Abbas; Dumitru Baleanu; Ghazala Akram; Maasoomah Sadaf; Mirfa Dawood; Muhammad Abbas; Dumitru Baleanu

doi:10.3934/math.2023219

AIMS Mathematics

2023, Volume 8, Issue 2: 4390-4406. doi: 10.3934/math.2023219

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Solitary wave solutions to Gardner equation using improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method

1.
Department of Mathematics, University of the Punjab, 54590 Lahore, Pakistan
2.
Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan
3.
Department of Mathematics, Cankaya University, 06530 Ankara, Turkey
4.
Institute of Space Science, Magurele-Bucharest, Romania
5.
Lebanese American University, 1102 2801 Beirut, Lebanon

Received: 30 August 2022 Revised: 30 September 2022 Accepted: 07 October 2022 Published: 05 December 2022
MSC : 49Q10, 53A04

In this study, the improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.
- exact solutions,
- solitary waves,
- gardner equation,
- exponential solution,
- rational function,
- solitons,
- hyperbolic solution,
- improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method
Citation: Ghazala Akram, Maasoomah Sadaf, Mirfa Dawood, Muhammad Abbas, Dumitru Baleanu. Solitary wave solutions to Gardner equation using improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method[J]. AIMS Mathematics, 2023, 8(2): 4390-4406. doi: 10.3934/math.2023219

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Abstract

In this study, the improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.

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