Quiescent Solitons in Magneto-Optic Waveguides with Nonlinear Chromatic Dispersion and Kudryashov’s Form of Self-Phase Modulation Having Generalized Temporal Evolution

  • Elsayed M.E. Zayed Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt https://orcid.org/0000-0002-6755-0088
  • Mona El–Shater Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt https://orcid.org/0000-0001-6587-1331
  • Ahmed H. Arnous Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India; Research Center of Applied Mathematics, Khazar University, Baku, Azerbaijan https://orcid.org/0000-0002-7699-7068
  • Omer Mohammed Khodayer Al-Dulaimi Department of Communication Technical Engineering, Al–Farahidi University, Baghdad, Iraq https://orcid.org/0000-0001-8581-0448
  • Farag Mahel Mohammed Al–Nibras University–Iraq, Tikrit, Iraq https://orcid.org/0000-0001-6391-2435
  • Ibrahim Zeghaiton Chaloob Department of Business Administration, College of Administration and Economics, Al–Esraa University, Baghdad, Iraq https://orcid.org/0000-0002-1741-5232
  • O. González-Gaxiola Applied Mathematics and Systems Department, Universidad Aut´onoma Metropolitana–Cuajimalpa, Mexico City, Mexico https://orcid.org/0000-0003-3317-9820
  • Anjan Biswas Department of Mathematics & Physics, Grambling State University, Grambling, LA , USA; Department of Physics and Electronics, Khazar University, Baku, Azerbaijan; Department of Applied Sciences, Cross–Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, Galati, Romania; Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, South Africa https://orcid.org/0000-0002-8131-6044
  • Carmelia Mariana Balanica Dragomir Department of Applied Sciences, Cross–Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, Galati, Romania https://orcid.org/0000-0001-7743-928X
DOI: https://doi.org/10.26565/2312-4334-2025-4-12
Keywords: Solitons, Self-Phase Modulation, Integrability, Chromatic Dispersion

Abstract

The article discusses how Kudryashov's proposed self-phase modulation scheme and nonlinear chromatic dispersion cause the evolution of quiescent optical solitons in magneto-optic waveguides. Provide a comprehensive understanding of the governing model; generalised temporal evolution is considered. The modified sub-ODE approach is employed to facilitate the recovery of such solitons. This leads to a complete range of optical solitons and the necessary conditions that must be met for these solitons to exist, which are also provided.

Downloads

Download data is not yet available.

References

H. Schamel, ”Quiescent solitary, snoidal and sinusoidal ion acoustic waves,” Plasma Phys. 14(10), 905–924 (1972). https://doi.org/10.1088/0032-1028/14/10/002

J.L. Hammack, ”A note on tsunamis: Their generation and propagation in an ocean of uniform depth,” J. Fluid Mech. 60(4), 769–799 (1973). https://doi.org/10.1017/S0022112073000479

A. Hasegawa, and F. Tappert, ”Transmission of quiescent nonlinear optical pulses in dispersive dielectric fibers. I. Anomalous dispersion,” Apple. Phys. Lett. 23(3), 142-144 (1973). https://doi.org/10.1063/1.1654836

M. Karlsson, and A. Hook, ”Soliton-like pulses governed by fourth order dispersion in optical fibers,” Opt. Commun. 104(4–6), 303–307 (1994). https://doi.org/10.1016/0030-4018(94)90560-6

D. Mihalache, D. Mazilu, B.A. Malomed, and L. Torner, ”Asymmetric spatio-temporal optical solitons in media with quadratic nonlinearity,” Opt. Commun. 152(4–6), 365–370 (1998). https://doi.org/10.1016/S0030-4018(98)00206-5

D. Mihalache, D. Mazilu, L.-C. Crasovan, L. Torner, B.A. Malomed, and F. Lederer, ”Three-dimensional walking spatiotemporal solitons in quadratic media,” Phys. Rev. E - Stat. Phys. Plasmas Fluids Rel. Interdiscip. Top. 62(5), 7340–7347 (2000). https://doi.org/10.1103/PhysRevE.62.7340

N.A. Kudryashov, ”Periodic and solitary waves in optical fiber Bragg gratings with dispersive reflectivity,” Chinese J. Phys. 66, 401–405 (2020). https://doi.org/10.1016/j.cjph.2020.06.006

W.C.K. Mak, B.A. Malomed, and P.L. Chu, ”Three-wave gap solitons in waveguides with quadratic nonlinearity,” Phys. Rev. E - Stat. Phys. Plasmas Fluids Rel. Interdiscip. Top. 58(5), 6708–6722 (1998). https://doi.org/10.1103/PhysRevE.58.6708

A.H. Arnous, A. Biswas, Y. Yıldırım, L. Moraru, M. Aphane, S.P. Moshokoa, and H.M. Alshehri, ”Quiescent optical solitons with Kudryashov’s generalized quintuple-power and nonlocal nonlinearity having nonlinear chromatic dispersion: generalized temporal evolution,” Ukr. J. Phys. Opt. 24(1), 105–113 (2023). https://doi.org/10.3116/16091833/24/2/105/2023

N.A. Kudryashov, ”Highly dispersive optical solitons of the generalized nonlinear eighth-order Schr¨odinger equation,” Optik, 206, 164335 (2020). https://doi.org/10.1016/j.ijleo.2020.164335

E.M.E. Zayed, R. Shohib, M. Alngar, A. Biswas, M. Ekici, S. Khan, A.K. Alzahrani, and M. Belic, ”Optical solitons and conservation laws associated with Kudryashov’s sextic power-law nonlinearity of refractive index,” Ukr. J. Phys. Opt. 22, 38–49 (2021). https://doi.org/10.3116/16091833/22/1/38/2021

A.R. Adem, M. Ekici, A. Biswas, M. Asmag, E.M.E. Zayed, A.K. Alzahrani, and M.R. Belic, ”Stationary optical solitons with nonlinear chromatic dispersion having quadratic–cubic law of refractive index,” Phys. Lett. A, 384, 126606 (2020). https://doi.org/10.1016/j.physleta.2020.126606

N. Sucu, M. Ekici, and A. Biswas, ”Quiescent optical solitons with nonlinear chromatic dispersion and generalized temporal evolution by extended trial function approach,” Chaos Solitons Fractals, 147, 110971 (2021). https://doi.org/10.1016/j.chaos.2021.110971

A.H. Arnous, T.A. Nofal, A. Biswas, S. Khan, and L. Moraru, ”Quiescent optical solitons with Kudryashov’s generalized quintuple-power and nonlocal nonlinearity having nonlinear chromatic dispersion,” Universe, 8, 501 (2022). https://doi.org/10.3390/universe8100501

M. Ekici, A. Sonmezoglu, and A. Biswas, ”Quiescent optical solitons with Kudryashov’s laws of refractive index,” Chaos Solitons Fractals, 151, 111226 (2021). https://doi.org/10.1016/j.chaos.2021.111226

A.R. Adem, B.P. Ntsime, A. Biswas, S. Khan, A.K. Alzahraniand, and M.R. Belic, ”Quiescent optical solitons with nonlinear chromatic dispersion for Lakshmanan–Porsezian–Daniel model having Kerr law of nonlinear refractive index,” Ukr. J. Phys. Opt. 22, 83–86 (2021). https://doi.org/10.3116/16091833/22/2/83/2021

A. Biswas, M. Ekici, and A. Sonmezoglu, ”Quiescent optical solitons with Kudryashov’s quintuple power–law of refractive index having nonlinear chromatic dispersion,” Phys. Lett. A, 426, 127885 (2022). https://doi.org/10.1016/j.physleta.2021.127885

A. Sonmezoglu, ”Stationary optical solitons having Kudryashov’s quintuple power law nonlinearity by extended G'/G -expansion,” Optik, 253, 168521 (2022). https://doi.org/10.1016/j.ijleo.2021.168521

N.A. Kudryashov, ”Mathematical model of propagation pulse in optical fiber with power nonlinearities,” Optik, 212, 164750 (2020). https://doi.org/10.1016/j.ijleo.2020.164750

N.A. Kudryashov, and E.V. Antonova, ”Solitary waves of equation for propagation pulse with power nonlinearities,” Optik, 217, 164881, (2020). https://doi.org/10.1016/j.ijleo.2020.164881

N.A. Kudryashov, ”Highly dispersive optical solitons of equation with various polynomial nonlinearity law,” Chaos Solitons Fractals 140, 110202, (2020). https://doi.org/10.1016/j.chaos.2020.110202

N.A. Kudryashov, ”Model of propagation pulses in an optical fiber with a new law of refractive indices,” Optik, 248, 168160, (2021). https://doi.org/10.1016/j.ijleo.2021.168160 https://doi.org/10.1016/j.physleta.2020.126606

A.R. Adem, B.P. Ntsime, A. Biswas, M. Asma, M. Ekici, S.P. Moshokoa, A.K. Alzahrani, and M.R. Belic, ”Quiescent optical solitons with Sasa–Satsuma equation having nonlinear chromatic dispersion,” Phys. Lett. A, 384, 126721 (2020). https://doi.org/10.1016/j.physleta.2020.126721

A. Biswas, M. Ekici, A. Sonmezoglu, and M. Belic, ”Quiescent optical solitons with nonlinear group velocity dispersion by extended trial function scheme,” Optik, 171, 529–542, (2018). https://doi.org/10.1016/j.ijleo.2018.06.067

A.H. Arnous, A. Biswas, Y. Yildirim, and A. Asiri, ”Quiescent optical solitons for the concatenation model having nonlinear chromatic dispersion with differential group delay,” Contemp. Math. 4(4), 877–904 (2023). https://doi.org/10.37256/cm.4420233596

Y. Geng, and J. Li, ”Exact solutions to a nonlinearly dispersive Schrodinger equation,” Appl. Math. Comp. 195, 420–439 (2008). https://doi.org/10.1016/j.amc.2007.04.119

Z. Yan, ”Envelope compactons and solitary patterns,” Phys. Lett. A, 355, 212–215 (2006). https://doi.org/10.1016/j.physleta.2006.02.032

Z. Yan, ”Envelope compact and solitary pattern structures for the GNLS(m,n,p,q) equations,” Phys. Lett. A, 357, 196–203 (2006). https://doi.org/10.1016/j.physleta.2006.04.032

Z. Yan, ”New exact solution structures and nonlinear dispersion in the coupled nonlinear wave systems,” Phys. Lett. A, 361, 194–200 (2007). https://doi.org/10.1016/j.physleta.2006.07.032

Z. Zhang, Z. Liu, X. Miao, andY. Chen, ”Qualitative analysis and travelingwave solutions for the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity,” Phys. Lett. A, 375, 1275–1280 (2011). https://doi.org/10.1016/j.physleta.2010.11.070

Z. Zhang, Y.-x. Li, Z.-h. Liu, and X.-j. Miao, ”New exact solutions to the perturbed nonlinear Schrodinger’s equation with Kerr law nonlinearity via modified trigonometric function series method,” Commun. Nonlin. Sci. Num. Simul. 16, 3097–3106, (2011). https://doi.org/10.1016/j.cnsns.2010.12.010

E.M.E. Zayed, M. El-Shater, A.H. Arnous, Y. Yıldırım, L. Hussein, A.J.M. Jawad, S.S. Veni, and A. Biswas, ”Quiescent optical solitons with Kudryashov’s generalized quintuple-power law and nonlocal nonlinearity having nonlinear chromatic dispersion with generalized temporal evolution by enhanced direct algebraic method and sub-ODE approach,” Eur. Phys. J. Plus, 139, 885 (2024). https://doi.org/10.1140/epjp/s13360-024-05636-8

N.A. Kudryashov, ”Stationary solitons of the generalized nonlinear Schr¨odinger equation with nonlinear dispersion and arbitrary refractive index,” Appl. Math. Lett. 128, 107888 (2022). https://doi.org/10.1016/j.aml.2021.107888

N.A. Kudryashov, ”Quiescent solitons of the model with nonlinear chromatic dispersion and arbitrary refractive index,” Optik, 259, 168888 (2022). https://doi.org/10.1016/j.ijleo.2022.168888

Z. Yang, and B.Y. Hon, ”An improved modified extended tanh-function method,” Zeitschrift fur Naturforschung A, 61(3-4), 103–115 (2007). https://doi.org/10.1515/zna-2006-3-401

E.M.E. Zayed, and M.E.M. Alngar, ”Application of newly proposed sub-ODE method to locate chirped optical solitons to Triki–Biswas equation,” Optik, 207, 164360 (2020). https://doi.org/10.1016/j.ijleo.2020.164360

Z.L. Li, ”Periodic Wave Solutions of a Generalized KdV-mKdV Equation with Higher-Order Nonlinear Terms,” Z. Naturforsch, 65a, 649-657 (2010). http://www.znaturforsch.com/s65a/s65a0649.pdf

E.M.E. Zayed, Kh.A. Gepreel, M.E.M. Alngar, A. Biswas, A. Dakova, M. Ekici, H.M. Alshehri, and M.R. Belic, ”Cubic–quartic solitons for twin-core couplers in optical metamaterials,” Optik, 245, 167632 (2021). https://doi.org/10.1016/j.ijleo.2021.167632

Y. Chen, and Z. Yan, ”The Weierstrass elliptic function expansion method and its applications in nonlinear wave equations,” Chaos, Soliton of Fractalas, 29, 948-964 (2006). https://doi.org/10.1016/j.chaos.2005.08.071

Y. Zhen-Ya, ”NewWeierstrass semi-rational expansion method to doubly periodic solutions of soliton equations,” Commu. Theor. Phys. 43, 391-396 (2005). https://doi.org/10.1007/s12596-024-01728-x

Published
2025-12-08
Cited
How to Cite
Zayed, E. M., El–Shater, M., Arnous, A. H., Al-Dulaimi, O. M. K., Mohammed, F. M., Chaloob, I. Z., González-Gaxiola, O., Biswas, A., & Dragomir, C. M. B. (2025). Quiescent Solitons in Magneto-Optic Waveguides with Nonlinear Chromatic Dispersion and Kudryashov’s Form of Self-Phase Modulation Having Generalized Temporal Evolution. East European Journal of Physics, (4), 141-156. https://doi.org/10.26565/2312-4334-2025-4-12
Issue
No. 4 (2025): East European Journal of Physics
Section
Original Papers

Copyright (c) 2025 Elsayed M.E. Zayed, Mona El–Shater, Ahmed H. Arnous, Omer Mohammed Khodayer Al-Dulaimid, Farag Mahel Mohammed, Ibrahim Zeghaiton Chaloob, O. González–Gaxiola, Anjan Biswas, Carmelia Mariana Balanica Dragomir

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Authors who publish with this journal agree to the following terms:

    • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
    • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
    • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).