Skip to main content
SpringerLink
Log in

New solitons and other exact wave solutions for coupled system of perturbed highly dispersive CGLE in birefringent fibers with polynomial nonlinearity law

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

The use of optical fiber for communication has grown at a rapid pace due to the demands of the modern information era. In this paper, the modified extended direct algebraic method is implemented to explore optical solitons and other exact wave solutions for the coupled system of perturbed highly dispersive complex Ginzburg–Landau equation with polynomial nonlinearity law which describe the transmission of solitons in birefringent fibers. The obtained solutions include bright solitons, dark solitons, singular solitons and combo dark-singular solitons. Additionally, Jacobi elliptic function solutions, exponential solutions, and singular periodic solutions are also offered. To ensure the existence of the obtained soliton solutions, we set some constraints on the parameters. In addition, some selected solutions are visually shown to demonstrate the physical properties of the exact solutions.

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

Similar content being viewed by others

Data availibility

There is no data set used.

References

  • Ahmed, H.M., Rabie, W.B.: Structure of optical solitons in magneto-optic waveguides with dual-power law nonlinearity using modified extended direct algebraic method. Opt. Quant. Electron. 53(8), 438 (2021)

    Google Scholar 

  • Ahmed, K.K., Badra, N.M., Ahmed, H.M., Rabie, W.B.: Soliton solutions and other solutions for Kundu–Eckhaus equation with quintic nonlinearity and Raman effect using the improved modified extended tanh-function method. Mathematics 10, 1–11 (2022)

    Google Scholar 

  • Ahmed, K.K., Badra, N.M., Ahmed, H.M., Rabie, W.B.: Soliton solutions of generalized Kundu–Eckhaus equation with an extra-dispersion via improved modified extended tanh-function technique. Opt. Quant. Electron. 55(299), 1–17 (2023)

    Google Scholar 

  • Aranson, I.S., Kramer, L.: The world of the complex Ginzburg–Landau equation. Rev. Mod. Phys. 74(1), 99 (2002)

    ADS  MathSciNet  Google Scholar 

  • Asjad, M.I., Ullah, N., Rehman, H., Inc, M.: Construction of optical solitons of magneto-optic waveguides with anti-cubic law nonlinearity. Opt. Quant. Electron. 53, 1–16 (2021)

    Google Scholar 

  • Biswas, A., Yildirim, Y., Yasar, E., Triki, H., Alshomrani, A.S., Ullah, M.Z., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical soliton perturbation for complex Ginzburg–Landau equation with modified simple equation method. Optik 158, 399–415 (2018)

    ADS  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with Kerr law nonlinearity by extended Jacobi’s elliptic function expansion. Optik 183, 395–400 (2019)

    ADS  Google Scholar 

  • Ekici, M.: Stationary optical solitons with complex Ginzburg–Landau equation having nonlinear chromatic dispersion and Kudryashov’s refractive index structures. Phys. Lett. A 440, 128146 (2022)

    MathSciNet  Google Scholar 

  • Fan, X., Qu, T., Huang, S., Chen, X., Cao, M., Zhou, Q., Liu, W.: Analytic study on the influences of higher-order effects on optical solitons in fiber laser. Optik 186, 326–331 (2019)

    ADS  Google Scholar 

  • Fendzi-Donfack, E., Kenfack-Jiotsa, A.: Extended Fan’s sub-ODE technique and its application to a fractional nonlinear coupled network including multicomponents-LC blocks. Chaos, Solitons & Fractals 177, 114266 (2023)

    MathSciNet  Google Scholar 

  • Fendzi-Donfack, E., Nguenang, J.P., Nana, L.: Fractional analysis for nonlinear electrical transmission line and nonlinear Schrödinger equations with incomplete sub-equation. The European Physical Journal Plus 133, 1–11 (2018)

    Google Scholar 

  • Fendzi-Donfack, E., Nguenang, J.P., Nana, L.: On the traveling waves in nonlinear electrical transmission lines with intrinsic fractional-order using discrete tanh method. Chaos, Solitons & Fractals 131, 109486 (2020)

    MathSciNet  Google Scholar 

  • Fendzi-Donfack, E., Nguenang, J.P., Nana, L.: On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission line. Nonlinear Dyn. 104, 691–704 (2021)

    Google Scholar 

  • Fendzi-Donfack, E., Kumar, D., Tala-Tebue, E., Nana, L., Nguenang, J.P., Kenfack-Jiotsa, A.: Construction of exotical soliton-like for a fractional nonlinear electrical circuit equation using differential-difference Jacobi elliptic functions sub-equation method. Results in Physics 32, 105086 (2022)

    Google Scholar 

  • Fendzi-Donfack, E., Temgoua, G.W.K., Djoufack, Z.I., Kenfack-Jiotsa, A., Nguenang, J.P., Nana, L.: Exotical solitons for an intrinsic fractional circuit using the sine-cosine method. Chaos, Solitons & Fractals 160, 112253 (2022)

    MathSciNet  Google Scholar 

  • Fendzi-Donfack, E., Tala-Tebue, E., Inc, M., Kenfack-Jiotsa, A., Nguenang, J.P., Nana, L.: Dynamical behaviours and fractional alphabetical-exotic solitons in a coupled nonlinear electrical transmission lattice including wave obliqueness. Opt. Quant. Electron. 55(1), 35 (2023)

    Google Scholar 

  • Fendzi-Donfack, E., Baduidana, M., Fotsa-Ngaffo, F., Kenfack-Jiotsa, A.: Construction of abundant solitons in a coupled nonlinear pendulum lattice through two discrete distinct techniques. Results in Physics 52, 106783 (2023)

    Google Scholar 

  • García-Morales, V., Krischer, K.: The complex Ginzburg–Landau equation: an introduction. Contemp. Phys. 53(2), 79–95 (2012)

    ADS  Google Scholar 

  • Ghayad, M.S., Badra, N.M., Ahmed, H.M., Rabie, W.B.: Derivation of optical solitons and other solutions for nonlinear Schrödinger equation using modified extended direct algebraic method. Alex. Eng. J. 64, 801–811 (2023)

    Google Scholar 

  • Gu, Y., Manafian, J., Malmir, S., Eslami, B., Ilhan, O.A.: Lump, lump-trigonometric, breather waves, periodic wave and multi-waves solutions for a Konopelchenko-Dubrovsky equation arising in fluid dynamics. Int. J. Mod. Phys. B 37(15), 2350141 (2023)

    ADS  Google Scholar 

  • Ilhan, O.A., Manafian, J.: Periodic type and periodic cross-kink wave solutions to the (2+ 1)-dimensional breaking soliton equation arising in fluid dynamics. Mod. Phys. Lett. B 33(23), 1950277 (2019)

    ADS  MathSciNet  Google Scholar 

  • Ilhan, O.A., Manafian, J., Lakestani, M., Singh, G.: Some novel optical solutions to the perturbed nonlinear Schrödinger model arising in nano-fibers mechanical systems. Mod. Phys. Lett. B 36(03), 2150551 (2022)

    ADS  Google Scholar 

  • Jiang, W., Wang, X., Huang, H., Zhang, D., Ghadimi, N.: Optimal economic scheduling of microgrids considering renewable energy sources based on energy hub model using demand response and improved water wave optimization algorithm. J. Energy Storage 55, 105311 (2022)

    Google Scholar 

  • Khalifa, A. S., Badra, N. M., Ahmed, H. M., Rabie, W. B.: Retrieval of optical solitons in fiber Bragg gratings for high-order coupled system with arbitrary refractive index, Optik, 171116 (2023)

  • Khalil, T.A., Badra, N., Ahmed, H.M., Rabie, W.B.: Optical solitons and other solutions for coupled system of nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index by Jacobi elliptic function expansion method. Optik 253, 168540 (2022)

    ADS  Google Scholar 

  • Kudryashov, N.A.: Optical solitons of a mathematical model with arbitrary refractive index. Optik 224, 165391 (2020)

    ADS  Google Scholar 

  • Li, C., Manafian, J., Eslami, B., Mahmoud, K. H., Abass, R. R., Bashar, B. S., Ilhan, O. A.: A generalized trial equation scheme: A tool for solving thin films constructed from the ferroelectric materials, International Journal of Modern Physics B, 2450308 (2023)

  • Li, D., Manafian, J., Ilhan, O.A., Alkhayyat, S., Mahmoud, K.H., Alsalamy, A., Zeynalli, S.M.: Solitary waves for the nonparaxial nonlinear Schrödinger equation. Mod. Phys. Lett. B 38(01), 2350204 (2024)

    ADS  Google Scholar 

  • Mehrpooya, M., Ghadimi, N., Marefati, M., Ghorbanian, S.A.: Numerical investigation of a new combined energy system includes parabolic dish solar collector, Stirling engine and thermoelectric device. Int. J. Energy Res. 45(11), 16436–16455 (2021)

    Google Scholar 

  • Mir, M., Shafieezadeh, M., Heidari, M.A., Ghadimi, N.: Application of hybrid forecast engine based intelligent algorithm and feature selection for wind signal prediction. Evol. Syst. 11, 559–573 (2020)

    Google Scholar 

  • Nestor, S., Abbagari, S., Houwe, A., Betchewe, G., Doka, S.Y.: Diverse chirped optical solitons and new complex traveling waves in nonlinear optical fibers. Commun. Theor. Phys. 72(6), 065501 (2020)

    ADS  MathSciNet  Google Scholar 

  • Ozisik, M., Cinar, M., Secer, A., Bayram, M.: Optical solitons with Kudryashov’s sextic power-law nonlinearity. Optik 261, 169202 (2022)

    ADS  Google Scholar 

  • Rabie, W.B., Ahmed, H.M.: Cubic-quartic optical solitons and other solutions for twin-core couplers with polynomial law of nonlinearity using the extended F-expansion method. Optik 253, 168575 (2022)

    ADS  Google Scholar 

  • Raza, N., Aslam, M.R., Rezazadeh, H.: Analytical study of resonant optical solitons with variable coefficients in Kerr and non-Kerr law media. Opt. Quant. Electron. 51, 1–12 (2019)

    Google Scholar 

  • Rehman, H. Ur., Ullah, N., Imran, M. A.: Highly dispersive optical solitons using Kudryashov’s method, Optik 199, (2019) 163349

  • Rizvi, S.T.R., Ahmed, S.: Resonant collisions among X-type, multi-lump, generalized breathers. N-solitons and rogue waves in plasma, Optik 292, 171390 (2023)

    Google Scholar 

  • Rizvi, S.T.R., Shabbir, S.: Optical soliton solution via complete discrimination system approach along with bifurcation and sensitivity analyses for the Gerjikov-Ivanov equation. Optik 294, 171456 (2023)

    ADS  Google Scholar 

  • Rizvi, S.T., Seadawy, A.R., Raza, U.: Chirped optical wave solutions for a nonlinear model with parabolic law and competing weakly nonlocal nonlinearities. Opt. Quant. Electron. 54(11), 756 (2022)

    Google Scholar 

  • Samir, I., Badra, N., Seadawy, A.R., Ahmed, H.M., Arnous, A.H.: Computational extracting solutions for the perturbed Gerdjikov–Ivanov equation by using improved modified extended analytical approach. J. Geom. Phys. 176, 104514 (2022)

    MathSciNet  Google Scholar 

  • Seadawy, A.R., Ahmed, H.M., Rabie, W.B., Biswas, A.: Chirp-free optical solitons in fiber Bragg gratings with dispersive reflectivity having polynomial law of nonlinearity. Optik 225, 165681 (2021)

    ADS  Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ahmed, S., Khaliq, A.: Pure-cubic nonlinear Schrödinger model with optical multi peak, homoclinic breathers, periodic-cross-kink and M-shaped solitons. Opt. Quant. Electron. 54(11), 771 (2022)

    Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ahmed, S., Ahmad, A.: Study of dissipative NLSE for dark and bright, multiwave, breather and M-shaped solitons along with some interactions in monochromatic waves. Opt. Quant. Electron. 54(12), 782 (2022)

    Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Ahmad, A.: Study of non-local Boussinesq dynamical equation for multiwave, homoclinic breathers and other rational solutions. Opt. Quant. Electron. 55(3), 278 (2023)

    Google Scholar 

  • Seadawy, A.R., Ahmad, A., Rizvi, S.T., Ahmed, S.: Bifurcation solitons, Y-type, distinct lumps and generalized breather in the thermophoretic motion equation via graphene sheets. Alex. Eng. J. 87, 374–388 (2024)

    Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Mustafa, B., Ali, K.: Applications of complete discrimination system approach to analyze the dynamic characteristics of the cubic-quintic nonlinear Schrodinger equation with optical soliton and bifurcation analysis. Results in Physics 56, 107187 (2024)

    Google Scholar 

  • Sonmezoglu, A.: Stationary optical solitons having Kudryashov’s quintuple power law nonlinearity by extended \(G^\prime /G\)-expansion. Optik 253, 168521 (2022)

    ADS  Google Scholar 

  • Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: New optical solitons based on the perturbed Chen–Lee–Liu model through Jacobi elliptic function method. Opt. Quant. Electron. 54(2), 131 (2022)

    Google Scholar 

  • Tedjani, A.H., Seadawy, A.R., Rizvi, S.T., Solouma, E.: Construction of chirped propagation with Jacobi elliptic functions for the nonlinear Schrödinger equations with quadratic nonlinearity with inter-modal and spatio-temporal dispersions. The European Physical Journal Plus 138(11), 973 (2023)

    ADS  Google Scholar 

  • Yıldırım, Y., Biswas, A., Dakova, A., Guggilla, P., Khan, S., Alshehri, H. M., Belic, M. R.: Cubic–quartic optical solitons having quadratic–cubic nonlinearity by sine–Gordon equation approach, Ukrainian Journal of Physical Optics 22(4), (2021)

  • Yu, D., Ghadimi, N.: Reliability constraint stochastic UC by considering the correlation of random variables with Copula theory. IET Renew. Power Gener. 13(14), 2587–2593 (2019)

    Google Scholar 

  • Zayed, E.M.E., Gepreel, K.A., El-Horbaty, M., Biswas, A., Yıldırım, Y., Alshehri, H.M.: Highly dispersive optical solitons with complex Ginzburg–Landau equation having six nonlinear forms. Mathematics 9, 3270 (2021)

    Google Scholar 

  • Zayed, E.M., Alngar, M.E., Shohib, R.M., Nofal, T.A., Gepreel, K.A.: Highly dispersive optical solitons in birefringent fibers for perturbed complex Ginzburg–Landau equation having polynomial law of nonlinearity. Optik 261, 169206 (2022)

    ADS  Google Scholar 

  • Zhang, S., Manafian, J., Ilhan, O. A., Jalil, A. T., Yasin, Y., Gatea, M. Abdulfadhil: Nonparaxial pulse propagation to the cubic-quintic nonlinear Helmholtz equation, International Journal of Modern Physics B, 2450117 (2023)

  • Zhao, N., Manafian, J., Ilhan, O.A., Singh, G., Zulfugarova, R.: Abundant interaction between lump and k-kink, periodic and other analytical solutions for the (3+1)-D Burger system by bilinear analysis. Int. J. Mod. Phys. B 35(13), 2150173 (2021)

    ADS  MathSciNet  Google Scholar 

Download references

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Author information

Authors and Affiliations

  1. Department of Physics and Engineering Mathematics, Higher Institute of Engineering and Technology, Tanta, Egypt

    Wafaa B. Rabie

  2. Department of Physics and Engineering Mathematics, Faculty of Engineering, Ain Shams University, Cairo, Abbassia, Egypt

    Karim K. Ahmed & Niveen M. Badra

  3. Department of Mathematics, Faculty of Basic Sciences, German University in Cairo (GUC), Cairo, Egypt

    Karim K. Ahmed

  4. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El Shorouk Academy, Cairo, Egypt

    Hamdy M. Ahmed

  5. Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, 44891-63157, Iran

    M. Mirzazadeh

  6. Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    M. Eslami

Authors
  1. Wafaa B. Rabie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karim K. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Niveen M. Badra
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hamdy M. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. Mirzazadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. M. Eslami
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Eslami.

Ethics declarations

Conflicts of interest

The authors declare that they have no conflict of interest.

Ethical Approval

The authors declare that there is no animal studies in this work.

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

Rabie, W.B., Ahmed, K.K., Badra, N.M. et al. New solitons and other exact wave solutions for coupled system of perturbed highly dispersive CGLE in birefringent fibers with polynomial nonlinearity law. Opt Quant Electron 56, 875 (2024). https://doi.org/10.1007/s11082-024-06644-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-024-06644-9

Keywords

Search

Navigation