Optical solitons for Biswas–Milovic equation using the new Kudryashov’s scheme

Altun, Selvi; Özişik, M.N.; Seçer, Aydın; Bayram, Mustafa

doi:10.1016/j.ijleo.2022.170045

Cited by 21 publications

(6 citation statements)

References 52 publications

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“…Comparing with other techniques such as unified Riccati equation expansion [30], Kudryashov's scheme [31,32], the direct mapping method [33] and F-expansion method [34], this method give various types of solutions such as bright, dark, singular solitons. In addition, other mathematical solutions such as exponential, Jacobi elliptic, Weierstrass elliptic, plane wave, rational type, hyperbolic, periodic and singular periodic solutions can be extracted.…”

Section: Procedures (3)mentioning

confidence: 99%

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

Samir,

El-Sham,

El-barkoki

et al. 2024

Contemp. Math.

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The presented research investigates the (2+1)-dimensional perturbed nonlinear Schrödinger model. This model takes into account various effects such as fourth order dispersion, intermodal dispersion, nonlinear dispersion, group velocity dispersion, Kerr nonlinearity and self steepening effects. This model simulates the estimation of optical solitons and a variety of broadcasting networks’ transmission in nonlinear fiber optics. The proposed model is studied using the improved modified extended tanh function technique. For the proposed model, several solitons and other solutions are generated. These solutions including {bright, dark and singular} solitons, singular periodic and Jacobi elliptic solutions. By introducing the two- and three-dimensional graphs, the physical behavior of the retrieved solutions is displayed.

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Section: Procedures (3)mentioning

confidence: 99%

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

Samir,

El-Sham,

El-barkoki

et al. 2024

Contemp. Math.

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“…Within the realm of optical fiber communication, the significance of the BME is notable, as it stands as a valuable tool for modeling diverse soliton solutions. These solitons represent solitary waves capable of traversing long distances without altering their form, a characteristic crucial for transmitting information without distortion [5,6]. Furthermore, their equations are integrable, indicating that they harbor an infinite number of conservation laws.…”

Section: Introductionmentioning

confidence: 99%

“…This investigation delves into the interaction between parabolic and power law nonlinearities within the framework of the BME. Here is the form of the BME [5]:…”

Section: Introductionmentioning

confidence: 99%

Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

Hossain,

Alsharif,

Miah

et al. 2024

Mathematics

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This study extensively explores the Biswas–Milovic equation (BME) with Kerr and power law nonlinearity to extract the unique characteristics of optical soliton solutions. These optical soliton solutions have different applications in the field of precision in optical switching, applications in waveguide design, exploration of nonlinear optical effects, imaging precision, reduced intensity fluctuations, suitability for optical signal processing in optical physics, etc. Through the powerful (G′/G, 1/G)-expansion analytical method, a variety of soliton solutions are expressed in three distinct forms: trigonometric, hyperbolic, and rational expressions. Rigorous validation using Mathematica software ensures precision, while dynamic visual representations vividly portray various soliton patterns such as kink, anti-kink, singular soliton, hyperbolic, dark soliton, and periodic bright soliton solutions. Indeed, a sensitivity analysis was conducted to assess how changes in parameters affect the exact solutions, aiding in the understanding of system behavior and informing decision-making, especially in accurately designing or analyzing real-world optical phenomena. This investigation reveals the significant influence of parameters λ, τ, c, B, and Κ on the precise solutions in Kerr and power law nonlinearities within the BME. Notably, parameter λ exhibits consistently high sensitivity across all scenarios, while parameters τ and c demonstrate pronounced sensitivity in scenario III. The outcomes derived from this method are distinctive and carry significant implications for the dynamics of optical fibers and wave phenomena across various optical systems.

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“…Plenty of studies have been carried out on different forms of BME. Such as BME with Kerr law nonlinearity [38], BME with dual-power law [39,40], BME having Kudryashovʼs law of arbitrary refractive [41,42], the perturbed BME with Kudryashovʼs law of refractive index, [43] a coupled system of BME having Kudryashovʼs law of arbitrary refractive [44], (2 + 1)-BME [45,46], (3 + 1)-BME [46], BME having parabolic law and STD [47,48] analyzes Lie symmetries for BME with power law nonlinearity. Depending on the importance of the BME equation, it is possible to add dozens of studies to this list, and these studies can be accessed with a simple literature review.…”

Section: Introductionmentioning

confidence: 99%

Optical solitons for the Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion

Özdemir

2023

Phys. Scr.

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For the first time, the optical soliton solutions of the $(1+1)$-dimensional Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion are intended to be analyzed in detail. To attain this purpose, the new Kudryashov and the Kudryashov auxiliary equation technique are successfully implemented. Moreover, the impacts of model parameters on the soliton dynamics are scrutinized. The complex wave transformation is utilized to get the nonlinear ordinary differential equation form and to generate soliton solutions, the presented methods are performed. Finally, various graphical illustrations were derived and detailed comments were added on the solution results. The new Kudryashov approach and the Kudryashov auxiliary equation technique have been successfully performed and soliton solutions obtained. W-shape soliton was acquired with the new Kudryashov approach and the bright soliton was acquired with the Kudryashov auxiliary equation technique. Furthermore, diverse graphic descriptions that the resulting soliton solutions are obtained, and 2D graphs are presented and commented on. Since the Biswas-Milovic equation, which is the subject of much research, has an important role in nonlinear optics, different forms of the Biswas-Milovic equation are developed in the literature. The model in the presence of spatio-temporal dispersion was presented and scrutinized for the first time.

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Optical solitons for Biswas–Milovic equation using the new Kudryashov’s scheme

Cited by 21 publications

References 52 publications

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

Extraction of Solitons in Optical Fibers for the (2+1)-Dimensional Perturbed Nonlinear Schrödinger Equation Via the Improved Modified Extended Tanh Function Technique

Abundant New Optical Soliton Solutions to the Biswas–Milovic Equation with Sensitivity Analysis for Optimization

Optical solitons for the Biswas-Milovic equation with anti-cubic law nonlinearity in the presence of spatio-temporal dispersion

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