Ukrainian Journal of Physical Optics


2026 Volume 27, Issue 3


ISSN 1816-2002 (Online), ISSN 1609-1833 (Print)

IMPLICIT QUIESCENT SOLITON PERTURBATION IN OPTICAL METAMATERIALS WITH NONLINEAR CHROMATIC DISPERSION AND KUDRYASHOV'S QUINTUPLE FORM OF SELF-PHASE MODULATION BY LIE SYMMETRY

A. R. Adem, A. H. Arnous, L. S. Calucag and A. Biswas

Author Information
1A. R. Adem ORCID logo SCOPUS logo, 2,3A. H. Arnous ORCID logo SCOPUS logo, 4L. S. Calucag SCOPUS logo, 5,6,7,8A. Biswas SCOPUS logo
1Department of Mathematical Sciences, University of South Africa, UNISA–0003, South Africa
2Department of Mathematical Sciences, Saveetha School of Engineering, SIMATS Chennai–602105, Tamilnadu, India
3Research Center of Applied Mathematics, Khazar University, Baku, AZ–1096, Azerbaijan
4Department of Mathematics and Science, University of Technology, Bahrain, Kingdom of Bahrain
5Department of Mathematics & Physics, Grambling State University, Grambling, LA 71245–2715, USA
6Department of Physics and Electronics, Khazar University, Baku AZ–1096, Azerbaijan
7Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa–0204, South Africa
8Applied Science Research Center, Applied Science Private University, Amman–11937, Jordan

ABSTRACT

The current paper addresses the formation of perturbed quiescent solitons in optical metamaterials with nonlinear chromatic dispersion for Kudryashov’s quintuple form of self-phase modulation by Lie symmetry. This work examines two models: the nonlinear Schrödinger equation and the complex Ginzburg–Landau equation, both with linear and generalized temporal evolution. The results are expressed in terms of quadratures, and the solition's existence criteria are also presented.

Keywords: quiescent solitons, metamaterials, chromatic dispersion

UDC: 535.32

About this Article
Original Manuscript: 29.12.2025
Revised Manuscript: 16.02.2026
Manuscript Accepted: 27.02.2026
Published (OnLine): 02.03.2026
Published (Print): be published
    1. Adem, A. R. Arnous, A. H. Ahmed, Husham M. & Biswas, A. (2026) "Implicit quiescent soliton perturbation in optical fibers with nonlinear chromatic dispersion and Kudryashov's quintuple form of self-phase modulation by Lie symmetry". To be published in Semiconductor Physics, Quantum Electronics & Optoelectronics. (to be published).
      doi:10.26565/2312-4334-2025-4-22
    2. Biswas, A., Ekici, M., Sonmezoglu, A., & Belic, M. (2018). Stationary optical solitons with nonlinear group velocity dispersion by extended trial function scheme. Optik, 171, 529-542.
      doi:10.1016/j.ijleo.2018.06.067
    3. Arnous, A. H., Biswas, A., Yıldırım, Y., Moraru, L., Moldovanu, S., Iticescu, C., Khan, S. & Alshehri, H. M. (2023, January). Quiescent optical solitons with quadratic-cubic and generalized quadratic-cubic nonlinearities. In Telecom (Vol. 4, No. 1, pp. 31-42). MDPI.
      doi:10.3390/telecom4010003
    4. Ekici, M. (2022). Stationary optical solitons with complex Ginzburg-Landau equation having nonlinear chromatic dispersion and Kudryashov's refractive index structures. Physics Letters A, 440, 128146.
      doi:10.1016/j.physleta.2022.128146
    5. Ekici, M. (2022). Kinky breathers, W-shaped and multi-peak soliton interactions for Kudryashov's quintuple power-law coupled with dual form of non-local refractive index structure. Chaos, Solitons & Fractals, 159, 112172.
      doi:10.1016/j.chaos.2022.112172
    6. Ekici, M. (2022). Optical solitons with Kudryashov's quintuple power-law coupled with dual form of non-local law of refractive index with extended Jacobi's elliptic function. Optical and Quantum Electronics, 54(5), 279.
      doi:10.1007/s11082-022-03657-0
    7. Ekici, M. (2023). Stationary optical solitons with Kudryashov's quintuple power law nonlinearity by extended Jacobi's elliptic function expansion. Journal of Nonlinear Optical Physics & Materials, 32(01), 2350008.
      doi:10.1142/S021886352350008X
    8. Han, T., Li, Z., Li, C., & Zhao, L. (2023). Bifurcations, stationary optical solitons and exact solutions for complex Ginzburg-Landau equation with nonlinear chromatic dispersion in non-Kerr law media. Journal of Optics, 52(2), 831-844.
      doi:10.1007/s12596-022-01041-5
    9. Kudryashov, N. A. (2022). Stationary solitons of the generalized nonlinear Schrödinger equation with nonlinear dispersion and arbitrary refractive index. Applied Mathematics Letters, 128, 107888.
      doi:10.1016/j.aml.2021.107888
    10. Kudryashov, N. A. (2022). Stationary solitons of the model with nonlinear chromatic dispersion and arbitrary refractive index. Optik, 259, 168888.
      doi:10.1016/j.ijleo.2022.168888
    11. Jawad, A., & Abu-AlShaeer, M. (2023). Highly dispersive optical solitons with cubic law and cubic-quintic-septic law nonlinearities by two methods. Al-Rafidain Journal of Engineering Sciences, 1-8.
      doi:10.61268/sapgh524
    12. Jihad, N., & Abd Almuhsan, M. (2023). Evaluation of impairment mitigations for optical fiber communications using dispersion compensation techniques. Al-Rafidain Journal of Engineering Sciences, 81-92.
      doi:10.61268/0dat0751
    13. Smertenko, P., Rudko, G., Maksimenko, Z., & Belyaev, A. (2025). Quantum physics and photoluminescence: contribution of the SPQEO. Semiconductor Physics, Quantum Electronics & Optoelectronics, 28(4), 389-393.
      doi:10.15407/spqeo28.04.389
    14. Veni, S. S., Mani Rajan, M. S., Biswas, A., & Alshomrani, A. S. (2024). Exploring the dynamic interplay of intermodal and higher order dispersion in nonlinear negative index metamaterials. Physica Scripta, 99(8), 085261.
      doi:10.1088/1402-4896/ad6352
    15. Yalçı, A. M., & Ekici, M. (2022). Stationary optical solitons with complex Ginzburg-Landau equation having nonlinear chromatic dispersion. Optical and Quantum Electronics, 54(3), 167.
      doi:10.1007/s11082-022-03557-3
    16. Veselago, V. G. (1967). The electrodynamics of substances with simultaneously negative values of and. Usp. Fiz. Nauk, 92(3), 517-526.
      doi:10.3367/UFNr.0092.196707d.0517
    17. Smith, D. R., Pendry, J. B., & Wiltshire, M. C. (2004). Metamaterials and negative refractive index. Science, 305(5685), 788-792.
      doi:10.1126/science.1096796
    18. Adem, A. R., González-Gaxiola, O., Arnous, A. H., Calucag, L. S., & Biswas, A. (2026, January). Implicit Quiescent Solitons in Optical Metamaterials with Nonlinear Chromatic Dispersion and an Array of Self-Phase Modulation Structures with Generalized Temporal Evolution by Lie Symmetry. In Telecom (Vol. 7, No. 1, p. 6). MDPI.
      doi:10.3390/telecom7010006

    У цій статті розглядається формування збурених спокійних солітонів в оптичних метаматеріалах з нелінійною хроматичною дисперсією для п'ятикратної форми фазової модуляції Кудряшова за допомогою симетрії Лі. Розглянуті дві моделі: нелінійне рівняння Шредінгера та комплексне рівняння Гінзбурга-Ландау, обидві з лінійною та узагальненою часовою еволюцією. Результати виражені в квадратурах, а також представлені критерії існування солітонів.

    Ключові слова: спокійні солітони, метаматеріали, хроматична дисперсія

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