W-shaped chirp free and chirped bright, dark solitons for perturbed nonlinear Schrodinger equation in nonlinear optical fibers.
Muniyappan, Annamalai Sharmila, Muthuvel Priya, Elumalai Kaviya Sumithra, Sekar Biswas, Anjan Yıldırım, Yakup Aphane, Maggie Moshokoa, Seithuti P. Alshehri, Hashim M.
Muniyappan, Annamalai
Sharmila, Muthuvel
Priya, Elumalai Kaviya
Sumithra, Sekar
Biswas, Anjan
Yıldırım, Yakup
Aphane, Maggie
Moshokoa, Seithuti P.
Alshehri, Hashim M.
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Abstract
Solitons are nonlinear localized waves that can be found in the field of optics. This is because of the nonlinear reaction of the medium. In the process of considering the nonlinearity of transmitted waves, specifically for solitons, numerous heterogeneous forms of mathematical techniques have been explored. In the most recent few decades, there has been a substantial upsurge in interest surrounding the study of nonlinear wave phenomena such as breather waves, solitons, rogue waves, and many other types of waves. Researchers in the fields of engineering and applied sciences have found that the process of extracting solitons with nonlinear partial differential equations (NLPDEs) is one of the most interesting and intriguing subjects to study [3–6]. This result was confirmed by a large number of the scientists and engineers who have worked in these fields. The transmission of digital information across optical fibres is the most significant technological usage of the soliton, and it is accomplished by using this pulse. The remarkable subject of nonlinear optics known as the optical soliton explores a wide range of topics, including birefringent crystals, meta-surfaces, optical couplers, optical fibres, and magneto-optics [7–12]. NLPDEs can be used to model a broad variety of difficult processes that arise in real life and can be applied across many scientific disciplines [1–6]. The phenomenal cosmos is made up of virtually an infinite number of fascinating nonlinear occurrences that act as complementary elements. During the process of mathematical formulation, the nonlinearity of the resulting complex dynamical systems emerges. The non linear Schrodinger equation (NLSE) is one of the most important nonlinear evolution equations (NLEEs). ¨The NLSE can be expressed in its most general form as a cubic nonlinearity, which has several applications in the research on waves in optical fibres [9,10]. The complicated forms of higher order with intent special of NLSEs have been prepared with a number of different genera of nonlinear variables. It is common knowledge that the NLSE plays a significant part in a variety of subfields of nonlinear research, including Bose–Einstein condensates [14], nonlinear optics [15–17], and water waves [13]. In particular, the NLSE is able to represent the propagation of a picosecond optical pulse through optical fibres [18]. Recent years have seen an increase in the number of researchers interested in obtaining chirped fem to second optical pulses for application in communication systems [19–24]. Goyal et al. [19] used self frequency shift (SFS) and self-steepening (SS) to characterise the chirped brilliant, double-kink, and dark solitons of the cubic-quintic (CQ) NLSE. These solitons are described as having the CQ-NLSE. Bright, kink, and dark solitons with nonlinear chirp are derived for the NLSE having SS and SFS effects [20,21]. Also, higher-order NLSEs with non-Kerr law components are taken into consideration in the process of researching chirped femtosecond optical pulses in optical fibres [22–24]. These chirped solitonic pulses are essential in the design of solitary wave-based communications links, fiber-optic amplifiers, and optical pulse compressors [25]. They have many applications in pulse amplification or compression, and these applications include a wide variety of compression and amplification techniques. The chirped and chirp free W-shaped dark and bright solitonic structures are secured in Section 2 by applying the Jacobi elliptic function (JEF) method. In this research, these findings are given and addressed in Section 3.
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Date
2022-10-03
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Estonian Academy publishers
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Keywords
Solitons, Jacobi elliptic function method, NLS equation, Differential equation