Retrieval of Optical Solitons with Anti-Cubic Nonlinearity

Muslum Ozisik, Aydin Secer, Mustafa Bayram, Anjan Biswas, Oswaldo González-Gaxiola, Luminita Moraru (), Simona Moldovanu, Catalina Iticescu, Dorin Bibicu and Abdulah A. Alghamdi
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Muslum Ozisik: Mathematical Engineering, Yildiz Technical University, Istanbul 34200, Turkey
Aydin Secer: Computer Engineering, Biruni University, Istanbul 34010, Turkey
Mustafa Bayram: Computer Engineering, Biruni University, Istanbul 34010, Turkey
Anjan Biswas: Department of Mathematics and Physics, Grambling State University, Grambling, LA 71245, USA
Oswaldo González-Gaxiola: Applied Mathematics and Systems Department, Universidad Autonoma Metropolitana–Cuajimalpa, Vasco de Quiroga 4871, Mexico City 05348, Mexico
Luminita Moraru: Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania
Simona Moldovanu: Department of Computer Science and Information Technology, Faculty of Automation, Computers, Electrical Engineering and Electronics, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania
Catalina Iticescu: Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Dunarea de Jos University of Galati, 47 Domneasca Street, 800008 Galati, Romania
Dorin Bibicu: Department of Business Administration, Faculty of Economics and Business Administration, Dunarea de Jos University of Galati, 59–61 Nicolae Balcescu Street, 800001 Galati, Romania
Abdulah A. Alghamdi: Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Mathematics, 2023, vol. 11, issue 5, 1-18

Abstract: Purpose: In this article, two main subjects are discussed. First, the nonlinear Schrödinger equation (NLSE) with an anti-cubic (AC) nonlinearity equation is examined, which has a great working area, importance and popularity among the study areas of soliton behavior in optical fibers, by using the enhanced modified extended tanh expansion method and a wide range of optical soliton solutions is obtained. Second, the effects of AC parameters on soliton behavior are examined for each obtained soliton type. Methodology: In order to apply the method, the non-linear ordinary differential equation form (NLODE) of the investigated NLSE-AC is obtained by applying the defined wave transformation. Then, with the help of the proposed algorithm for the NLODE form, polynomial form, an algebraic equation system is obtained by setting the coefficients of this form to zero, and the solution of this system is also obtained. After determining the suitable solution set, the optical soliton solution of the investigated problem is obtained with the help of the serial form of the proposed method, a Riccati solution and wave transform. After checking that the solution satisfies the investigated problem, 3D and 2D graphics are obtained for the special parameter values and the necessary comments are made in the relevant sections. Findings: With the proposed method, many optical soliton solutions, such as topological, anti-peaked, combined peaked-bright, combined anti-peaked dark, singular, combined singular-anti peaked, periodic singular, composite kink anti-peaked, kink, periodic and periodic, with different amplitudes are obtained, and 3D and 2D representations have been made. Then, the effect of AC parameters on the soliton behavior in each case has been successfully studied. It has been shown that AC parameters have a significant effect on the soliton behavior, and this effect changes depending on the soliton shape and the parameters. Moreover, providing and maintaining the delicate balance between the soliton shape and the parameters and the interaction of the parameters with each other involves great difficulties. Originality: Although some soliton types of the NLSE-AC equation have been presented for the first time in this study, there is no study in the literature showing the effect of AC parameters on soliton behavior, especially for the NLSE-AC equation.

Keywords: AC non-linearity; delicate balance; enhanced modified extended tanh expansion; optical fiber; solitons (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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