J. Eur. Opt. Society-Rapid Publ. 2025, 21, 11 Ó The Author( s), published by EDP Sciences, 2025 https:// doi. org / 10.1051 / jeos / 2025005 Available online at: https:// jeos. edpsciences. org
Journal of the European Optical Society-Rapid Publications
RESEARCH ARTICLE
Sub-pico-second chirped optical solitons in birefringent fibers for space – time fractional Kaup-Newell equation
Khalil S. Al-Ghafri 1,*
, Anjan Biswas 2, 3, 4, 5, and Yakup Yıldırım 6, 7 1 Mathematics and Computing Skills Unit, University of Technology and Applied Sciences, PO Box 466, Ibri 516, Oman 2 Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245-2715, USA 3 Mathematical Modeling and Applied Computation( MMAC) Research Group, Center of Modern Mathematical Sciences
and their Applications( CMMSA), Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia 4 Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201 Galati, Romania 5 Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa 0204, Pretoria, South Africa 6 Department of Computer Engineering, Biruni University, Istanbul, 34010, Turkey 7 Department of Mathematics, Near East University, 99138, Nicosia, Cyprus
Received 3 November 2024 / Accepted 21 January 2025
Abstract. The present work is devoted to investigate the chirped bright and dark optical solitons of fractional Kaup-Newell equation( KNE) in birefringent fibers. The study is carried out analytically by the traveling wave hypothesis with the conformable derivative which reduces the governing model to an ordinary differential equation( ODE). The obtained equation is handled with the aid of an exotic integration scheme that utilizes the Jacobi elliptic equation in the form of a first-order nonlinear ODE with three-degree terms. Taking the modulus of Jacobi elliptic function to unity, distinct types of bright and dark optical solitons are derived with their corresponding chirping. The fractional order derivative is noted to have a significant influence on the pulse propagation. Additionally, the nonlinearity amount causes also marked variations in the amplitude and width of solitons. The modulation instability of the KNE is reported by implementing the linear stability analysis which confirms that all solutions are stable. The revealed results can be capitalized in improving the relevant physical and engineering applications in the field of birefringent fiber.
Keywords: Chirped solitons, Fractional Kaup-Newell equation, Jacobi elliptic equation method, Modulation instability.
1 Introduction
The recent research studies of optical pulses focus mainly on the dynamical features of propagating solitons in different optical fiber systems and other photonic media [ 1 – 4 ]. In addition, there are different fields of sciences that exploit soliton phenomena in applications such as quantum electronics [ 5 – 7 ], solid state physics [ 8, 9 ], Bose-Einstein condensates [ 10 – 16 ] and others. Understanding the physical properties of optical solitons can help to overcome the data over-demand that contribute in many applications in science, technology, and industry. Based on the continuous studies, scientists and engineers have reached an effective innovative tool known as birefringent fiber that possesses an optical property of light polarization enhancing higher
* Corresponding author: khalil. alghafri @ utas. edu. om transmission speeds. Birefringence is a mechanism in which the light passes through certain materials and is split into two rays having different index of refraction. Due to its prominent significancy in various scientific applications, this phenomena has attained wide attention in the fields of fiber-optic communication system, fiber lasers, and fiber sensors [ 17 ]. In optical communication systems, for instance, birefringence fiber can play a vital role in transmitting light signals for long distance with minimal degradation, resulting in more reliable communication. Hence, a lot of studies in literature have intensively discussed the pulse propagation in birefringent fiber.
The dynamic features of optical solitons are dominated by the nonlinear Schrödinger equation( NLSE) and its analogous types of models with various forms of nonlinear refractive index. For example, Menyuk [ 18, 19 ] examined the birefringence impact on soliton propagation in
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