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

Ghazala Akram; Saima Arshed; Maasoomah Sadaf; Hajra Mariyam; Muhammad Nauman Aslam; Riaz Ahmad; Ilyas Khan; Jawaher Alzahrani; Ghazala Akram; Saima Arshed; Maasoomah Sadaf; Hajra Mariyam; Muhammad Nauman Aslam; Riaz Ahmad; Ilyas Khan; Jawaher Alzahrani

doi:10.3934/math.2023413

AIMS Mathematics

2023, Volume 8, Issue 4: 8171-8184. doi: 10.3934/math.2023413

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Research article

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

1.
Department of Mathematics, University of the Punjab, Lahore, Pakistan
2.
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
3.
Department of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, China
4.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia

Received: 14 October 2022 Revised: 04 December 2022 Accepted: 26 December 2022 Published: 01 February 2023

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 $ \frac{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 $ 3 $D-surface plots and the corresponding $ 2 $D-contour graphs.
Citation: Ghazala Akram, Saima Arshed, Maasoomah Sadaf, Hajra Mariyam, Muhammad Nauman Aslam, Riaz Ahmad, Ilyas Khan, Jawaher Alzahrani. Abundant solitary wave solutions of Gardner's equation using three effective integration techniques[J]. AIMS Mathematics, 2023, 8(4): 8171-8184. doi: 10.3934/math.2023413

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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 $ \frac{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 $ 3 $D-surface plots and the corresponding $ 2 $D-contour graphs.

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