Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

Ayesha Mahmood; Hari Mohan Srivastava; Muhammad Abbas; Farah Aini Abdullah; Pshtiwan Othman Mohammed; Dumitru Baleanu; Nejmeddine Chorfi

doi:10.1016/j.heliyon.2023.e20852

Optical soliton solutions of the coupled Radhakrishnan-Kundu-Lakshmanan equation by using the extended direct algebraic approach

Heliyon. 2023 Oct 13;9(10):e20852. doi: 10.1016/j.heliyon.2023.e20852. eCollection 2023 Oct.

Authors

Ayesha Mahmood¹, Hari Mohan Srivastava^{2

3

4}, Muhammad Abbas¹, Farah Aini Abdullah⁵, Pshtiwan Othman Mohammed⁶, Dumitru Baleanu^{7

8

9}, Nejmeddine Chorfi¹⁰

Affiliations

¹ Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan.
² Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada.
³ Center for Converging Humanities, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Republic of Korea.
⁴ Section of Mathematics, International Telematic University Uninettuno, I-00186 Rome, Italy.
⁵ School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia.
⁶ Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq.
⁷ Department of Computer Science and Mathematics, Lebanese American University, Beirut 11022801, Lebanon.
⁸ Institute of Space Sciences, R76900 Magurele-Bucharest, Romania.
⁹ Department of Medical Research, China Medical University, Taichung 40402, Taiwan.
¹⁰ Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.

Abstract

The analytical soliton solutions place a lot of value on birefringent fibres. The major goal of this study is to generate novel forms of soliton solutions for the Radhakrishnan-Kundu-Lakshmanan equation, which depicts unstable optical solitons that arise from optical propagations using birefringent fibres. The (presumably new) extended direct algebraic (EDA) technique is used here to extract a large number of solutions for RKLE. It gives soliton solutions up to thirty-seven, which essentially correspond to all soliton families. This method's ability to determine many sorts of solutions through a single process is one of its key advantages. Additionally, it is simple to infer that the technique employed in this study is really straightforward yet one of the quite effective approaches to solving nonlinear partial differential equations so, this novel extended direct algebraic (EDA) technique may be regarded as a comprehensive procedure. The resulting solutions are found to be hyperbolic, periodic, trigonometric, bright and dark, combined bright-dark, and W-shaped soliton, and these solutions are visually represented by means of 2D, 3D, and density plots. The present study can be extended to investigate several other nonlinear systems to understand the physical insights of the optical propagations through birefringent fibre.

Keywords: 26A48; 26A51; 33B10; 39A12; 39B62; Birefringent fibres; Extended direct algebraic (EDA) technique; Optical solitons; Radhakrishnan-Kundu-Lakshmanan equation (RKLE); Soliton solutions.