Probing Families of Optical Soliton Solutions in Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model with Improved Versions of Extended Direct Algebraic Method

• Published in: Fractal and fractional Vol. 7; no. 7; p. 512
• Main Authors: Yasmin, Humaira, Aljahdaly, Noufe H., Saeed, Abdulkafi Mohammed, Shah, Rasool
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.07.2023
• Subjects: Algebra; Communications systems; Data processing; Domestic relations; Extended Direct Algebraic Method; Fiber optics; Fractional Perturbed Radhakrishnan Kundu Lakshmanan Model; generalized trigonometric functions; Investigations; Methods; Nonlinear optics; Nonlinear Ordinary Differential Equation; Nonlinear systems; Numerical analysis; optical soliton solutions; Optics; Ordinary differential equations; Partial differential equations; Solitary waves; variable transformation
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract7070512

In this investigation, we utilize advanced versions of the Extended Direct Algebraic Method (EDAM), namely the modified EDAM (mEDAM) and r+ mEDAM, to explore families of optical soliton solutions in the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model (FPRKLM). Our study stands out due to its in-depth investigation and the identification of multiple localized and stable soliton families, illuminating their complex behavior. We offer visual validation via carefully designed 3D graphics that capture the complex behaviors of these solitons. The implications of our research extend to fiber optics, communication systems, and nonlinear optics, with the potential for driving developments in optical devices and information processing technologies. This study conveys an important contribution to the field of nonlinear optics, paving the way for future advancements and a greater comprehension of optical solitons and their applications.