Bifurcation analysis and optical soliton solutions of the ion sound and Langmuir wave equation using the modified Khater method

Marium Khadim; Muhammad Abbas; Tahir Nazir; Alina Alb Lupas; Muhammad Nadeem Anwar; M. R. Alharthi; Marium Khadim; Muhammad Abbas; Tahir Nazir; Alina Alb Lupas; Muhammad Nadeem Anwar; M. R. Alharthi

doi:10.3934/math.2025875

AIMS Mathematics

2025, Volume 10, Issue 8: 19617-19641. doi: 10.3934/math.2025875

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Bifurcation analysis and optical soliton solutions of the ion sound and Langmuir wave equation using the modified Khater method

1.
Department of Mathematics, University of Sargodha, 40100 Sargodha, Pakistan; leomarium135@gmail.com, tahir.nazir@uos.edu.pk
2.
Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, Romania
3.
Institute of Education, University of Sargodha, 40100 Sargodha, Pakistan; nadeem.anwar@uos.edu.pk
4.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia; muteb@tu.edu.sa

Received: 27 May 2025 Revised: 21 July 2025 Accepted: 07 August 2025 Published: 27 August 2025
MSC : 34G20, 35A20, 35A22, 35R11

This research work focused on the modified Khater method to obtain the optical soliton solutions of the ion sound and Langmuir wave equation. The modified Khater approach, which produces a wide variety of solutions for the model under consideration, is regarded as one of the most modern and accurate analytical approach for non-linear evolution equations. The wave transformation was used to translate the governing model into an ordinary differential equation. The optical soliton solutions that were developed exhibit many waveforms, including singular periodic shape, sharp dark soliton, kink, and anti-kink soliton solutions. The outcomes may have a significant impact on applications in mathematical physics and engineering. Using the wave transformation, the dynamical system of the governing equation was obtained, and the theory of the planar dynamical system was used to carry out its bifurcation. The existence of chaotic behaviors in the suggested model was examined by taking into account a perturbed term in the resulting dynamical system. Furthermore, the dynamical system's sensitivity analysis was analyzed.
- modified Khater method,
- bifurcation,
- ion sound and Langmuir wave model,
- soliton solution
Citation: Marium Khadim, Muhammad Abbas, Tahir Nazir, Alina Alb Lupas, Muhammad Nadeem Anwar, M. R. Alharthi. Bifurcation analysis and optical soliton solutions of the ion sound and Langmuir wave equation using the modified Khater method[J]. AIMS Mathematics, 2025, 10(8): 19617-19641. doi: 10.3934/math.2025875

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Abstract

This research work focused on the modified Khater method to obtain the optical soliton solutions of the ion sound and Langmuir wave equation. The modified Khater approach, which produces a wide variety of solutions for the model under consideration, is regarded as one of the most modern and accurate analytical approach for non-linear evolution equations. The wave transformation was used to translate the governing model into an ordinary differential equation. The optical soliton solutions that were developed exhibit many waveforms, including singular periodic shape, sharp dark soliton, kink, and anti-kink soliton solutions. The outcomes may have a significant impact on applications in mathematical physics and engineering. Using the wave transformation, the dynamical system of the governing equation was obtained, and the theory of the planar dynamical system was used to carry out its bifurcation. The existence of chaotic behaviors in the suggested model was examined by taking into account a perturbed term in the resulting dynamical system. Furthermore, the dynamical system's sensitivity analysis was analyzed.

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