Skip to main content
SpringerLink
Log in

Soliton solutions of perturbed NLSE-CQ model in polarization-preserving fibers with cubic–quintic–septic–nonic nonlinearities

  • Research Article
  • Published:
Journal of Optics Aims and scope Submit manuscript

Abstract

This article aims to explore the diverse cubic–quintic–septic–nonic nonlinear solitary wave solutions within perturbed nonlinear Schrödinger equations occurring in polarization-preserving fibers. To achieve this, we employ a combination of Kudryashov’s method and an innovative mapping technique. Through these methods, we not only identify but also demonstrate various novel types of solitary wave solutions, along with their respective parameter constraints. The results present a wide spectrum of soliton solutions, encompassing straddled, bright, dark, and singular solitons. The study’s discoveries hold significant relevance in domains such as optical communications and fiber optics, where a thorough comprehension of solitary wave characteristics is pivotal for optimizing signal transmission and processing. Moreover, these findings offer potential benefits in the realm of nonlinear optics and the development of optical devices, empowering us to fine-tune and govern optical signals for a multitude of technological advancements. The study’s incorporation of numerical simulations amplifies its worth, rendering it a valuable asset for both theoretical research and real-world applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. N.A. Kudryashov, A. Biswas, A.H. Kara, Y. Yıldırım, Cubic–quartic optical solitons and conservation laws having cubic–quintic–septic–nonic self-phase modulation. Optik 269, 169834 (2022)

    Article  ADS  Google Scholar 

  2. D. Chen, Z. Li, Optical solitons of the cubic–quartic–nonlinear Schrödinger’s equation having cubic–quintic–septic–nonic form of self-phase modulation. Optik 277, 170687 (2023)

    Article  ADS  Google Scholar 

  3. I. Samir, A.H. Arnous, Y. Yıldırım, A. Biswas, L. Moraru, S. Moldovanu, Optical solitons with cubic–quintic–septic–nonic nonlinearities and quadrupled power-law nonlinearity: an observation. Mathematics 10, 4085 (2022)

    Article  Google Scholar 

  4. M.Y. Wang, Highly dispersive optical solitons of perturbed nonlinear Schrödinger equation with Kudryashov’s sextic-power law nonlinear. Optik 267, 169631 (2022)

    Article  ADS  Google Scholar 

  5. M.Y. Wang, Optical solitons with perturbed complex Ginzburg–Landau equation in Kerr and cubic–quintic–septic nonlinearity. Results Phys. 33, 105077 (2022)

    Article  Google Scholar 

  6. A. Biswas, S. Konar, Soliton perturbation theory for the compoundKdV equation. Int. J. Theor. Phys. 46, 237–243 (2007)

    Article  MATH  Google Scholar 

  7. A. Biswas, S. Konar, Soliton perturbation theory for the generalized Benjamin–Bona–Mahoney equation. Commun. Nonlinear Sci. Numer. Simul. 13, 703–706 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. A. Biswas, Optical soliton perturbation with nonlineardamping and saturable amplifiers. Math. Comput. Simul. 56, 521–537 (2001)

    Article  MATH  Google Scholar 

  9. A. Biswas, Soliton perturbation theory for Alfven waves in plasmas. Phys. Plasmas 12, 798 (2005)

    Article  MathSciNet  Google Scholar 

  10. A. Biswas, Optical soliton perturbation with bandwidth limited amplification and saturable amplifiers. J. Nonlinear Opt. Phys. Mater. 8, 277–288 (1999)

    Article  ADS  Google Scholar 

  11. Z.Y. Zhang, Z.H. Liu, X.J. Miao, Y.Z. Chen, New exact solutions to the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity. Appl. Math. Comput. 216, 3064–3072 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Biswas, M. Fessak, S. Johnson, S. Beatrice, D. Milovic, Z. Jovanoski, R. Kohl, F. Majid, Optical soliton perturbation in non-Kerr law media: traveling wave solution. Opt. Laser Technol. 44, 263–268 (2012)

    Article  ADS  Google Scholar 

  13. S. Nestor, G. Betchewe, M. Inc, S.Y. Doka, Exact traveling wave solutions to the higher-order nonlinear Schrdinger equation having Kerr nonlinearity form using two strategic integrations. Eur. Phys. J. Plus 135, 1–13 (2020)

    Article  Google Scholar 

  14. A. Biswas, S. Arshed, Application of semi inverse variational principle to cubic–quartic optical solitons having Kerr and power law non-linearity. Optik 172, 847–50 (2018)

    Article  ADS  Google Scholar 

  15. O. Gonzalez-Gaxiola, A. Biswas, F. Mallawi, M.R. Belic, Cubic–quartic bright optical solitons with improved Adomian decomposition method. J. Adv. Res. 21, 161–167 (2020)

    Article  Google Scholar 

  16. Y. Yildirima, A. Biswas, A.J.M. Jawad, M. Ekici, Q. Zhou, S. Khan, A.K. Alzahrani, M.R. Belic, Cubic–quartic optical solitons in birefringent fibers with four forms of nonlinear refractive index by exp-function expansion. Results Phys. 16, 102913 (2020)

    Article  Google Scholar 

  17. X. Zeng, X. Yong, A new mapping method and its applications to nonlinear partial differential equations. Phys. Lett. A 372, 6602–6607 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  18. S.A. AlQahtani, M.E.M. Alngar, R.M. Shohib, P. Pathak, Highly dispersive embedded solitons with quadratic \(\chi ^{(}2)\) and cubic \(\chi ^{(}3)\) non-linear susceptibilities having multiplicative white noise via Itô calculus. Chaos Solitons Fract. 171, 113498 (2023)

    Article  Google Scholar 

  19. Y. Yıldırım, A. Biswas, M. Ekici, S. Khan, A.K. Alzahrani, M.R. Belic, Optical soliton perturbation with Kudryashov’s law of arbitrary refractive index. J. Opt. 50, 245–252 (2021)

    Article  Google Scholar 

  20. Y. Yıldırım, A. Biswas, A.H. Kara, M. Ekici, E.M. Zayed, A.K. Alzahrani, M.R. Belic, Optical solitons and conservation law with Kudryashov’s form of arbitrary refractive index. J. Opt. 50, 542–547 (2021)

    Article  MATH  Google Scholar 

  21. O. Gonzalez-Gaxiola, A. Biswas, M. Ekici, S. Khan, Highly dispersive optical solitons with quadratic-cubic law of refractive index by the variational iteration method. J. Opt. 51, 29–36 (2022)

    Article  Google Scholar 

  22. E.M.E. Zayed, A. Al-Nowehy, M.E.M. Alngar, A. Biswas, M. Asma, M. Ekici, A.K. Alzahrani, M.R. Belic, Highly dispersive optical solitons in birefringent fibers with four nonlinear forms using Kudryashov’s approach. J. Opt. 50, 120–131 (2021)

    Article  Google Scholar 

  23. J. Vega-Guzman, A. Biswas, M. Asma, A.R. Seadawy, M. Ekici, A.K. Alzahrani, M.R. Belic, Optical soliton perturbation with parabolic-nonlocal combo nonlinearity: undetermined coefficients and semi-inverse variational principle. J. Opt. 51, 22–28 (2022)

    Article  Google Scholar 

  24. Y. Yıldırım, E. Topkara, A. Biswas, H. Triki, M. Ekici, P. Guggilla, S. Khan, M.R. Belic, Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by sine-Gordon equation approach. J. Opt. 50, 322–329 (2021)

    Article  Google Scholar 

  25. Y. Yildirim, A. Biswas, A. Kara, M. Ekici, A. Alzahrani, M. Belic, Cubic–quartic optical soliton perturbation and conservation laws with generalized Kudryashov’s form of refractive index. J. Opt. India 50(3), 354–360 (2021)

    Article  MATH  Google Scholar 

  26. Y. Yıldırım, A. Biswas, H. Triki, M. Ekici, P. Guggilla, S. Khan, L. Moraru, M.R. Belic, Cubic–quartic optical soliton perturbation with Kudryashov’s law of refractive index having quadrupled-power law and dual form of generalized nonlocal nonlinearity by sine-Gordon equation approach. J. Opt. 50, 593–599 (2021)

    Article  Google Scholar 

  27. E.M.E. Zayed, M.E.M. Alngar, A. Biswas, A.H. Kara, L. Moraru, M. Ekici, A.K. Alzahrani, M.R. Belic, Solitons and conservation laws in magneto-optic waveguides with triple-power law nonlinearity. J. Opt. 49, 584–590 (2020)

    Article  Google Scholar 

  28. E.M.E. Zayed, R.M.A. Shohib, M.E.M. Alngar, A. Biswas, Y. Yıldırım, A. Asiri, Optical solitons with DWDM topology having parabolic law nonlinearity with multiplicative white noise. J. Opt. 66, 1–9 (2023). https://doi.org/10.1007/s12596-023-01370-z

    Article  Google Scholar 

  29. E.M.E. Zayed, A.H. Arnous, A. Biswas, Y. Yıldırım, A. Asiri, Optical solitons for the concatenation model with multiplicative white noise. J. Opt. 66, 1–10 (2023). https://doi.org/10.1007/s12596-023-01381-w

    Article  Google Scholar 

  30. A.H. Arnous, M. Mirzazadeh, A. Biswas, Y. Yıldırım, H. Triki, A. Asiri, A wide spectrum of optical solitons for the dispersive concatenation model. J. Opt. 66, 1–27 (2023). https://doi.org/10.1007/s12596-023-01383-8

    Article  Google Scholar 

  31. A.H. Arnous, A. Biswas, A.H. Kara, Y. Yıldırım, C.M.B. Dragomir, A. Asiri, Optical solitons and conservation laws for the concatenation model in the absence of self-phase modulation. J. Opt. 66, 1–24 (2023). https://doi.org/10.1007/s12596-023-01392-7

    Article  Google Scholar 

  32. A.R. Adem, B.P. Ntsime, A. Biswas, S. Khan, A.K. Alzahrani, M.R. Belic, Stationary optical solitons with nonlinear chromatic dispersion for Lakshmanan–Porsezian–Daniel model having Kerr law of nonlinear refractive index. Ukr. J. Phys. Opt. 22(2), 83–86 (2021)

    Article  Google Scholar 

  33. A.K. Alzahrani, M.R. Belic, Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by semi-inverse variational principle. Ukr. J. Phys. Opt. 22, 123 (2021)

    Article  Google Scholar 

  34. Y. Yıldırım, A. Biswas, P. Guggilla, S. Khan, H.M. Alshehri, M.R. Belic, Optical solitons in fibre Bragg gratings with third-and fourth-order dispersive reflectivities. Ukr. J. Phys. Opt. 22(4), 239–254 (2021)

    Article  Google Scholar 

  35. Y. Yildrim, A. Biswas, A. Dakova, P. Guggilla, S. Khan, H.M. Alshehri, M.R. Belic, Cubic–quartic optical solitons having quadratic–cubic nonlinearity by sine-Gordon equation approach. Ukr. J. Phys. Opt. 22(4), 255–269 (2021)

  36. E.M.E. Zayed, R.M.A. Shohib, M.E.M. Alngar, A. Biswas, Y. Yıldırım, A. Dakova, H.M. Alshehri, M.R. Belic, Optical solitons in the Sasa–Satsuma model with multiplicative noise via Itô calculus. Ukr. J. Phys. Opt. 23(1), 9–14 (2022)

    Article  Google Scholar 

  37. Y. Yıldırım, A. Biswas, S. Khan, M.F. Mahmood, H.M. Alshehri, Highly dispersive optical soliton perturbation with Kudryashov’s sextic-power law of nonlinear refractive index. Ukr. J. Phys. Opt. 23(1), 24–29 (2022)

    Article  Google Scholar 

  38. O. González-Gaxiola, A. Biswas, Y. Yildirim, H.M. Alshehri, Highly dispersive optical solitons in birefringent fibres with non) local form of nonlinear refractive index: Laplace–Adomian decomposition. Ukr. J. Phys. Opt. 23(2), 68–76 (2022)

    Article  Google Scholar 

  39. A.A. Al Qarni, A.M. Bodaqah, A.S.H.F. Mohammed, A.A. Alshaery, H.O. Bakodah, A. Biswas, Cubic–quartic optical solitons for Lakshmanan–Porsezian–Daniel equation by the improved Adomian decomposition scheme. Ukr. J. Phys. Opt. 23(4), 228–242 (2022)

  40. A.A. Al Qarni, A.M. Bodaqah, A.S.H.F. Mohammed, A.A. Alshaery, H.O. Bakodah, A. Biswas, Dark and singular cubic–quartic optical solitons with Lakshmanan–Porsezian–Daniel equation by the improved Adomian decomposition scheme. Ukr. J. Phys. Opt. 24(1), 46–61 (2023)

  41. A.H. Arnous, A. Biswas, Y. Yıldırım, L. Moraru, M. Aphane, S.P. Moshokoa, 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(2), 105 (2023)

    Article  Google Scholar 

  42. A. Kukkar, S. Kumar, S. Malik, A. Biswas, Y. Yıldırım, S.P. Moshokoa, S. Khan, A.A. Alghamdi, Optical solitons for the concatenation model with Kurdryashov’s approaches. Ukr. J. Phys. Opt. 24(2), 155–160 (2023)

    Article  Google Scholar 

  43. A. Biswas, J.M. Vega-Guzman, Y. Yildirim, S.P. Moshokoa, M. Aphane, A.A. Alghamdi, Optical solitons for the concatenation model with power-law nonlinearity: undetermined coefficients. Ukr. J. Phys. Opt. 24(3), 185–192 (2023)

    Article  Google Scholar 

  44. O. González-Gaxiola, A. Biswas, J.R.D. Chavez, A. Asiri, Bright and dark optical solitons for the concatenation model by the Laplace–Adomian decomposition scheme. Ukr. J. Phys. Opt. 24(3), 222–234 (2023)

    Article  Google Scholar 

  45. R. Kumar, R. Kumar, A. Bansal, A. Biswas, Y. Yildirim, S.P. Moshokoa, A. Asiri, Optical solitons and group invariants for Chen–Lee–Liu equation with time-dependent chromatic dispersion and nonlinearity by Lie symmetry. Ukr. J. Phys. Opt. 24(4), 04021–04029 (2023)

    Article  Google Scholar 

  46. E.M.E. Zayed, R.M.A. Shohib, A. Biswas, Y. Yakup, A. Maggie, S.P. Moshokoa, S. Khan, A. Asiri, Gap solitons with cubic–quartic dispersive reflectivity and parabolic law of nonlinear refractive index. Ukr. J. Phys. Opt. 24(4), 04030–04045 (2023)

    Article  Google Scholar 

  47. R.M.A. Shohib, M.E.M. Alngar, A. Biswas, Y. Yildirim, H. Triki, L. Moraru, C. Iticescu, P.L. Georgescu, A. Asiri, Optical solitons in magneto-optic waveguides for the concatenation model. Ukr. J. Phys. Opt. 24(3), 248–261 (2023)

    Article  Google Scholar 

  48. A.H. Arnous, A. Biswas, Y. Yakup, L. Moraru, C. Iticescu, P.L. Georgescu, A. Asiri, Optical solitons and complexitons for the concatenation model in birefringent fibers. Ukr. J. Phys. Opt. 24(4), 04060–04086 (2023)

    Article  Google Scholar 

  49. E.M.E. Zayed, M.E.M. Alngar, R.M. Shohib, A. Biswas, Y. Yildirim, L. Moraru, P.L. Georgescu, C. Iticescu, A. Asiri, Highly dispersive solitons in optical couplers with metamaterials having Kerr law of nonlinear rfractive index. Ukr. J. Phys. Opt. 25(1), 01001–01019 (2024)

    Article  Google Scholar 

  50. E.M.E. Zayed, M.E.M. Alngar, R.M. Shohib, A. Biswas, Y. Yildirim, C.M.B. Dragomir, Highly dispersive gap solitons in optical fibers with dispersive reflectivity having parabolic-nonlocal nonlinearity. Ukr. J. Phys. Opt. 25(1), 01033–01044 (2024)

    Article  Google Scholar 

  51. A.M. Elsherbeny, M. Mirzazadeh, A.H. Arnous, A. Biswas, Y. Yildirim, A. Dakova, A. Asiri, Optical bullets and domain walls with cross spatio-dispersion and having Kudryashov’s form of self-phase modulation. Contemp. Math. 4(3), 505–517 (2023)

    Article  Google Scholar 

  52. E.M. Zayed, K.A. Gepreel, M. El-Horbaty, A. Biswas, Y. Yildirim, H. Triki, A. Asiri, Optical solitons for the dispersive concatenation model. Contemp. Math. 4(3), 592–611 (2023)

    Article  Google Scholar 

  53. P. Albayrak, M. Ozisik, M. Bayram, A. Secer, S.E. Das, A. Biswas, Y. Yıldırım, M. Mirzazadeh, A. Asiri, Pure-cubic optical solitons and stability analysis with Kerr law nonlinearity. Contemp. Math. 4(3), 530–548 (2023)

    Article  Google Scholar 

  54. A.R. Adem, A. Biswas, Y. Yildirim, A. Asiri, Implicit quiescent optical solitons for the dispersive concatenation model with nonlinear chromatic dispersion by lie symmetry. Contemp. Math. 4(4), 666–674 (2023)

    Article  Google Scholar 

  55. S.A. AlQahtani, M.S. Al-Rakhami, R.M.A. Shohib, M.E.M. Alngar, P. Pathak, Dispersive optical solitons with Schrödinger–Hirota equation using the P\(^{6}\)-model expansion approach. Opt. Quantum Electron. 55(8), 701 (2023)

    Article  Google Scholar 

  56. E.M.E. Zayed, R.M.A. Shohib, A. Al-Nowehy, On solving the (3+1)-dimensional NLEQZK equation and the (3+1)-dimensional NLmZK equation using the extended simplest equation method. Comput. Math. Appl. 78, 3390–3407 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  57. E.M.E. Zayed, R.M.A. Shohib, A. Al-Nowehy, Solitons and other solutions for higher-order NLS equation and quantum ZK equation using the extended simplest equation method. Comput. Math. Appl. 76(9), 2286–2303 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  58. E.M.E. Zayed, M.E.M. Alngar, R.M.A. Shohib, Cubic–quartic embedded solitons with \(\chi ^{(}2)\) and cubic \(\chi ^{(}3)\) nonlinear susceptibilities having multiplicative white noise via Itô calculus. Chaos Solitons Fract. 168, 113186 (2023)

    Article  Google Scholar 

  59. E.M.E. Zayed, M.E.M. Alngar, R.M.A. Shohib, Dispersive optical solitons to stochastic resonant NLSE with both spatio-temporal and inter-modal dispersions having multiplicative white noise. Mathematics 10(17), 3197 (2022)

    Article  Google Scholar 

  60. E.M.E. Zayed, R.M.A. Shohib, M.E.M. Alngar, Cubic–quartic optical solitons in Bragg gratings fibers for NLSE having parabolic non-local law nonlinearity using two integration schemes. Opt. Quantum Electron. 53(8), 452 (2021)

    Article  Google Scholar 

Download references

Acknowledgements

The authors extend their appreciation to the Deputyship for Research & Innovation, Ministry of Education in Saudi Arabia for funding this research (IFKSURC-1-7107).

Author information

Authors and Affiliations

  1. New Emerging Technologies and 5G Network and Beyond Research Chair, Department of Computer Engineering, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia

    Salman A. AlQahtani

  2. Basic Science Department, Faculty of Computers and Artificial Intelligence, Modern University for Technology and Information, Cairo, 11585, Egypt

    Mohamed E. M. Alngar

Authors
  1. Salman A. AlQahtani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed E. M. Alngar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Salman A. AlQahtani or Mohamed E. M. Alngar.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

AlQahtani, S.A., Alngar, M.E.M. Soliton solutions of perturbed NLSE-CQ model in polarization-preserving fibers with cubic–quintic–septic–nonic nonlinearities. J Opt (2023). https://doi.org/10.1007/s12596-023-01526-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12596-023-01526-x

Keywords

Search

Navigation