Retrieval of solitons in birefringent optical fibers in communication systems with the effect of conformable fractional derivative using an analytic approach

Altaf Alshuhail; Hamdy M. Ahmed; Abeer S. Khalifa; Wael W. Mohammed; Mohamed S Algolam; Athar I Ahmed; Karim K. Ahmed; Altaf Alshuhail; Hamdy M. Ahmed; Abeer S. Khalifa; Wael W. Mohammed; Mohamed S Algolam; Athar I Ahmed; Karim K. Ahmed

doi:10.3934/math.2025771

AIMS Mathematics

2025, Volume 10, Issue 7: 17248-17273. doi: 10.3934/math.2025771

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Retrieval of solitons in birefringent optical fibers in communication systems with the effect of conformable fractional derivative using an analytic approach

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, El Shorouk City, Cairo, Egypt
3.
Department of Mathematics, Faculty of Basic Sciences, The German University in Cairo (GUC), Cairo, Egypt
4.
Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt

Received: 16 June 2025 Revised: 23 July 2025 Accepted: 28 July 2025 Published: 31 July 2025
MSC : 35R11, 35C05, 35C07, 35C08

This work is the first to study the concatenation model with conformable fractional derivatives in birefringent fibres, and we give a rich spectrum of optical soliton solutions and many other exact solutions. This concatenation model describes the propagation of solitons in birefringent optical fibres. To achieve this retrieval, the improved modified extended (IME) tanh function technique is utilized, an integration method that generates several soliton solutions and numerous additional solutions. The method captures complicated nonlinear dynamics with greater flexibility than traditional models, providing new insights into pulse propagation characteristics in current optical communication systems. The emergence of soliton solutions automatically determines the respective parameter conditions, which can be easily derived from the types of solution. Outcomes produce a variety of wave forms like bright, dark, and singular solitons, exponential, rational, singular periodic, Jacobi elliptic function solutions, and others. Additionally, the solutions found are utilized to produce a number of interesting 2D and 3D graphs.
- solitons,
- NLPDEs,
- IME tanh function algorithm,
- concatenation,
- birefringence,
- conformable fractional derivatives
Citation: Altaf Alshuhail, Hamdy M. Ahmed, Abeer S. Khalifa, Wael W. Mohammed, Mohamed S Algolam, Athar I Ahmed, Karim K. Ahmed. Retrieval of solitons in birefringent optical fibers in communication systems with the effect of conformable fractional derivative using an analytic approach[J]. AIMS Mathematics, 2025, 10(7): 17248-17273. doi: 10.3934/math.2025771

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Abstract

This work is the first to study the concatenation model with conformable fractional derivatives in birefringent fibres, and we give a rich spectrum of optical soliton solutions and many other exact solutions. This concatenation model describes the propagation of solitons in birefringent optical fibres. To achieve this retrieval, the improved modified extended (IME) tanh function technique is utilized, an integration method that generates several soliton solutions and numerous additional solutions. The method captures complicated nonlinear dynamics with greater flexibility than traditional models, providing new insights into pulse propagation characteristics in current optical communication systems. The emergence of soliton solutions automatically determines the respective parameter conditions, which can be easily derived from the types of solution. Outcomes produce a variety of wave forms like bright, dark, and singular solitons, exponential, rational, singular periodic, Jacobi elliptic function solutions, and others. Additionally, the solutions found are utilized to produce a number of interesting 2D and 3D graphs.

References

[1]	B. Guo, L. Ling, Q. P. Liu, Nonlinear Schrödinger equation: Generalized Darboux transformation and rogue wave solutions, Phys. Rev. E, 85 (2012), 026607. https://doi.org/10.1103/PhysRevE.85.026607 doi: 10.1103/PhysRevE.85.026607
[2]	D. W. Zuo, Y. T. Gao, L. Xue, Y. J. Feng, Lax pair, roguewave and soliton solutions for a variable-coefficient generalized nonlinear Schrödinger equation in an optical fiber, fluid or plasma, Opt. Quant. Electron., 48 (2016), 1–4. https://doi.org/10.1007/s11082-015-0290-3 doi: 10.1007/s11082-015-0290-3
[3]	N. A. Kudryashov, Embedded solitons of the generalized nonlinear Schrödinger equation with high dispersion, Regul. Chaotic Dyn., 27 (2022), 680–696. https://doi.org/10.1134/S1560354722060065 doi: 10.1134/S1560354722060065
[4]	N. H. Ali, S. A. Mohammed, J. Manafian, Study on the simplified MCH equation and the combined KdV-mKdV equations with solitary wave solutions, Part. Differ. Equ. Appl. Math., 9 (2024), 100599. https://doi.org/10.1016/j.padiff.2023.100599 doi: 10.1016/j.padiff.2023.100599
[5]	K. K. Ahmed, N. M. Badra, H. M. Ahmed, W. B. Rabie, Unveiling optical solitons and other solutions for fourth-order (2+1)-dimensional nonlinear Schrödinger equation by modified extended direct algebraic method, J. Optics, 2024, 1–13. https://doi.org/10.1007/s12596-024-01690-8 doi: 10.1007/s12596-024-01690-8
[6]	T. Y. Wang, Q. Zhou, W. J. Liu, Soliton fusion and fission for the high-order coupled nonlinear Schrödinger system in fiber lasers, Chinese Phys. B, 31 (2022), 020501. https://doi.org/10.1088/1674-1056/ac2d22 doi: 10.1088/1674-1056/ac2d22
[7]	S. Kumar, N. Mann, Abundant closed-form solutions of the (3+1)-dimensional Vakhnenko-Parkes equation describing the dynamics of various solitary waves in ocean engineering, J. Ocean Eng. Sci., 17 (2022). https://doi.org/10.1016/j.joes.2022.04.007 doi: 10.1016/j.joes.2022.04.007
[8]	K. K. Ahmed, H. M. Ahmed, N. M. Badra, W. B. Rabie, Optical solitons retrieval for an extension of novel dual-mode of a dispersive non-linear Schrödinger equation, Optik, 307 (2024), 171835. https://doi.org/10.1016/j.ijleo.2024.171835 doi: 10.1016/j.ijleo.2024.171835
[9]	Q. Zhou, Y. Sun, H. Triki, Y. Zhong, Z. Zeng, M. Mirzazadeh, Study on propagation properties of one-soliton in a multimode fiber with higher-order effects, Results Phys., 41 (2022), 105898. https://doi.org/10.1016/j.rinp.2022.105898 doi: 10.1016/j.rinp.2022.105898
[10]	K. K. Ahmed, N. M. Badra, H. M. Ahmed, W. B. Rabie, M. Mirzazadeh, M. Eslami, et al., Investigation of solitons in magneto-optic waveguides with Kudryashov's law nonlinear refractive index for coupled system of generalized nonlinear Schrödinger's equations using modified extended mapping method, Nonlinear Anal.-Model., 29 (2024), 205–223. https://doi.org/10.15388/namc.2024.29.34070 doi: 10.15388/namc.2024.29.34070
[11]	A. S. Khalifa, H. M. Ahmed, N. M. Badra, W. B. Rabie, Exploring solitons in optical twin-core couplers with Kerr law of nonlinear refractive index using the modified extended direct algebraic method, Opt. Quant. Electron., 56 (2024), 1060. https://doi.org/10.1007/s11082-024-06882-x doi: 10.1007/s11082-024-06882-x
[12]	A. S. Khalifa, N. M. Badra, H. M. Ahmed, W. B. Rabie, Retrieval of optical solitons in fiber Bragg gratings for high-order coupled system with arbitrary refractive index, Optik, 287 (2023), 171116. https://doi.org/10.1016/j.ijleo.2023.171116 doi: 10.1016/j.ijleo.2023.171116
[13]	Q. Zhou, Q. Zhu, A. Biswas, Optical solitons in birefringent fibers with parabolic law nonlinearity, Opt. Appl., 44 (2014), 399–409. https://doi.org/10.5277/oa140305 doi: 10.5277/oa140305
[14]	L. Cheng, Y. Zhang, W. X. Ma, An extended (2+1)-dimensional modified Korteweg-de Vries–Calogero–Bogoyavlenskii–Schiff equation: Lax pair and Darboux transformation, Commun. Theor. Phys., 77 (2024), 035002. https://doi.org/10.1088/1572-9494/ad84d3 doi: 10.1088/1572-9494/ad84d3
[15]	J. Ahmad, S. Akram, S. U. Rehman, N. B. Turki, N. A. Shah, Description of soliton and lump solutions to M-truncated stochastic Biswas–Arshed model in optical communication, Results Phys., 51 (2023), 106719. https://doi.org/10.1016/j.rinp.2023.106719 doi: 10.1016/j.rinp.2023.106719
[16]	M. Shakeel, N. A. Shah, J. D. Chung, Application of modified exp-function method for strain wave equation for finding analytical solutions, Ain Shams Eng. J., 14 (2023), 101883. https://doi.org/10.1016/j.asej.2022.101883 doi: 10.1016/j.asej.2022.101883
[17]	W. X. Ma, M. Chen, Direct search for exact solutions to the nonlinear Schrödinger equation, Appl. Math. Comput., 215 (2009), 2835–2842. https://doi.org/10.1016/j.amc.2009.09.024 doi: 10.1016/j.amc.2009.09.024
[18]	W. X. Ma, J. H. Lee, A transformed rational function method and exact solutions to the (3+1)-dimensional Jimbo–Miwa equation, Chaos Soliton. Fract., 42 (2009), 1356–1363. https://doi.org/10.1016/j.chaos.2009.03.043 doi: 10.1016/j.chaos.2009.03.043
[19]	A. Ankiewicz, N. Akhmediev, Higher-order integrable evolution equation and its soliton solutions, Phys. Lett. A, 378 (2014), 358–361. https://doi.org/10.1016/j.physleta.2013.11.031 doi: 10.1016/j.physleta.2013.11.031
[20]	A. Ankiewicz, Y. Wang, S. Wabnitz, N. Akhmediev, Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions, Phys. Rev. E, 89 (2014), 012907. https://doi.org/10.1103/PhysRevE.89.012907 doi: 10.1103/PhysRevE.89.012907
[21]	O. G. Gaxiola, A. Biswas, Y. Yildirim, A. S. Alshomrani, Bright optical solitons for the concatenation model with power-law nonlinearity: Laplace-Adomian decomposition, Contemp. Math., 2023, 1234–1248. https://doi.org/10.37256/cm.4420233705 doi: 10.37256/cm.4420233705
[22]	A. Biswas, J. V. Guzman, A. H. Kara, S. Khan, H. Triki, O. G. Gaxiola, et al., Optical solitons and conservation laws for the concatenation model: Undetermined coefficients and multipliers approach, Universe, 9 (2023), 15. https://doi.org/10.3390/universe9010015 doi: 10.3390/universe9010015
[23]	H. Triki, Y. Sun, Q. Zhou, A. Biswas, Y. Yıldırım, H. M. Alshehri, Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects, Chaos Soliton. Fract., 164 (2022), 112622. https://doi.org/10.1016/j.chaos.2022.112622 doi: 10.1016/j.chaos.2022.112622
[24]	M. Y. Wang, A. Biswas, Y. Yıldırım, L. Moraru, S. Moldovanu, H. M. Alshehri, Optical solitons for a concatenation model by trial equation approach, Electronics, 12 (2023), 19. https://doi.org/10.3390/electronics12010019 doi: 10.3390/electronics12010019
[25]	S. Kumar, S. K. Dhiman, Lie symmetry analysis, optimal system, exact solutions and dynamics of solitons of a (3+1)-dimensional generalised BKP-Boussinesq equation, Pramana-J. Phys., 96 (2022), 31. https://doi.org/10.1007/s12043-021-02269-9 doi: 10.1007/s12043-021-02269-9
[26]	H. Kumar, A. Malik, F. Chand, Analytical spatiotemporal soliton solutions to (3+1)-dimensional cubic-quintic nonlinear Schrödinger equation with distributed coefficients, J. Math. Phys., 53 (2012), 103704. https://doi.org/10.1063/1.4754433 doi: 10.1063/1.4754433
[27]	H. Bulut, T. A. Sulaiman, H. M. Baskonus, On the new soliton and optical wave structures to some nonlinear evolution equations, Eur. Phys. J. Plus, 132 (2017), 459. https://doi.org/10.1140/epjp/i2017-11738-7 doi: 10.1140/epjp/i2017-11738-7
[28]	E. M. Zayed, A. G. A. Nowehy, M. E. Elshater, Solitons and other solutions to nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity using several different techniques, Eur. Phys. J. Plus, 132 (2017), 1–4. https://doi.org/10.1140/epjp/i2017-11527-4 doi: 10.1140/epjp/i2017-11527-4
[29]	K. K. Ahmed, H. M. Ahmed, N. M. Badra, M. Mirzazadeh, W. B. Rabie, M. Eslami, Diverse exact solutions to Davey–Stewartson model using modified extended mapping method, Nonlinear Anal.-Model., 29 (2024), 983–1002. https://doi.org/10.15388/namc.2024.29.36103 doi: 10.15388/namc.2024.29.36103
[30]	M. A. S. Murad, Formation of optical soliton wave profiles of nonlinear conformable Schrödinger equation in weakly non-local media: Kudryashov auxiliary equation method, J. Opt., 2024. https://doi.org/10.1007/s12596-024-02110-7 doi: 10.1007/s12596-024-02110-7
[31]	A. S. Khalifa, H. M. Ahmed, N. M. Badra, W. B. Rabie, F. M. A. Askar, W. W. Mohammed, New soliton wave structure and modulation instability analysis for nonlinear Schrödinger equation with cubic, quintic, septic, and nonic nonlinearities, AIMS Math., 9 (2024), 26166–26181. https://doi.org/10.3934/math.20241278 doi: 10.3934/math.20241278
[32]	A. Biswas, J. V. Guzman, Y. Yıldırım, L. Moraru, C. Iticescu, A. A. Alghamdi, Optical solitons for the concatenation model with differential group delay: Undetermined coefficients, Mathematics, 11 (2023), 2012. https://doi.org/10.3390/math11092012 doi: 10.3390/math11092012
[33]	M. S. Ullah, M. Z. Ali, H. O. Roshid, Bifurcation, chaos, and stability analysis to the second fractional WBBM model, PLoS One, 19 (2024), e0307565. https://doi.org/10.1371/journal.pone.0307565 doi: 10.1371/journal.pone.0307565
[34]	M. Eslami, Exact traveling wave solutions to the fractional coupled nonlinear Schrödinger equations, Appl. Math. Comput., 285 (2016), 141–148. https://doi.org/10.1016/j.amc.2016.03.032 doi: 10.1016/j.amc.2016.03.032
[35]	R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264 (2014), 65–70. https://doi.org/10.1016/j.cam.2014.01.002 doi: 10.1016/j.cam.2014.01.002
[36]	Z. Yang, B. Y. Hon, An improved modified extended tanh-function method, Z. Naturforsch. A, 61 (2006), 103–115. https://doi.org/10.1515/zna-2006-3-401 doi: 10.1515/zna-2006-3-401
[37]	M. Ekici, C. A. Sarmaşık, Various dynamic behaviors for the concatenation model in birefringent fibers, Opt. Quant. Electron., 56 (2024), 1342. https://doi.org/10.1007/s11082-024-07252-3 doi: 10.1007/s11082-024-07252-3
[38]	E. U. Ekici, H. Triki, Stochastic perturbation of analytical solutions for the dispersive concatenation model with spatio-temporal dispersion having multiplicative white noise, Nonlinear Dynam., 113 (2025), 4325–4353. https://doi.org/10.1007/s11071-024-10560-8 doi: 10.1007/s11071-024-10560-8

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