Bifurcation, chaotic behavior and soliton solutions to the KP-BBM equation through new Kudryashov and generalized Arnous methods

Chander Bhan; Ravi Karwasra; Sandeep Malik; Sachin Kumar; Ahmed H. Arnous; Nehad Ali Shah; Jae Dong Chung; Chander Bhan; Ravi Karwasra; Sandeep Malik; Sachin Kumar; Ahmed H. Arnous; Nehad Ali Shah; Jae Dong Chung

doi:10.3934/math.2024424

AIMS Mathematics

2024, Volume 9, Issue 4: 8749-8767. doi: 10.3934/math.2024424

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Research article Special Issues

Bifurcation, chaotic behavior and soliton solutions to the KP-BBM equation through new Kudryashov and generalized Arnous methods

1.
Department of Mathematics and Statistics, Central University of Punjab, Bathinda, Punjab 151401, India
2.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy 11837, Cairo, Egypt
3.
Department of Mechanical Engineering, Sejong University, Seoul 05006, South Korea

Received: 26 November 2023 Revised: 08 January 2024 Accepted: 24 January 2024 Published: 29 February 2024
MSC : 35A09, 35A24, 35C08

This research paper investigates the Kadomtsev-Petviashvii-Benjamin-Bona-Mahony equation. The new Kudryashov and generalized Arnous methods are employed to obtain the generalized solitary wave solution. The phase plane theory examines the bifurcation analysis and illustrates phase portraits. Finally, the external perturbation terms are considered to reveal its chaotic behavior. These findings contribute to a deeper understanding of the dynamics of the Kadomtsev-Petviashvii-Benjamin-Bona-Mahony wave equation and its applications in real-world phenomena.
- bifurcation analysis,
- new Kudryashov method,
- exact solutions,
- generalized Arnous method,
- Kadomtsev-Petviashvii-Benjamin-Bona-Mahony (KP-BBM) equation,
- chaotic behavior
Citation: Chander Bhan, Ravi Karwasra, Sandeep Malik, Sachin Kumar, Ahmed H. Arnous, Nehad Ali Shah, Jae Dong Chung. Bifurcation, chaotic behavior and soliton solutions to the KP-BBM equation through new Kudryashov and generalized Arnous methods[J]. AIMS Mathematics, 2024, 9(4): 8749-8767. doi: 10.3934/math.2024424

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Abstract

This research paper investigates the Kadomtsev-Petviashvii-Benjamin-Bona-Mahony equation. The new Kudryashov and generalized Arnous methods are employed to obtain the generalized solitary wave solution. The phase plane theory examines the bifurcation analysis and illustrates phase portraits. Finally, the external perturbation terms are considered to reveal its chaotic behavior. These findings contribute to a deeper understanding of the dynamics of the Kadomtsev-Petviashvii-Benjamin-Bona-Mahony wave equation and its applications in real-world phenomena.

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