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Research Article | Open Access

Abundant solitary wave solutions of Gardner's equation using three effective integration techniques

Ghazala Akram1Saima Arshed1Maasoomah Sadaf1Hajra Mariyam1Muhammad Nauman Aslam2Riaz Ahmad3( )Ilyas Khan4Jawaher Alzahrani4
Department of Mathematics, University of the Punjab, Lahore, Pakistan
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
Department of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
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Abstract

Gardner's equation has been discussed in the article for finding new solitary wave solutions. Three efficient integration techniques, namely, the Kudryashov's R function method, the generalized projective Ricatti method and G G 2 -expansion method are implemented to obtain new dark soliton, bright soliton, singular soliton, and combo soliton solutions. Moreover, some of the obtained solutions are graphically depicted by using 3D-surface plots and the corresponding 2D-contour graphs.

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AIMS Mathematics
Pages 8171-8184

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Cite this article:
Akram G, Arshed S, Sadaf M, et al. Abundant solitary wave solutions of Gardner's equation using three effective integration techniques. AIMS Mathematics, 2023, 8(4): 8171-8184. https://doi.org/10.3934/math.2023413

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Received: 14 October 2022
Revised: 04 December 2022
Accepted: 26 December 2022
Published: 15 April 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)