Skip to main content
SpringerLink
Log in

The generalized Sasa–Satsuma equation and its optical solitons

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

Abstract

The principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa–Satsuma (GSS) equation describing the propagation of the femtosecond pulses in the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa–Satsuma equation, is firstly reduced in a one-dimensional real regime through a specific transformation; then, its bright and dark optical solitons are established using the modified Kudryashov (MK) method. The changes in the amplitude of the bright and dark solitons are analyzed as a case study for various classes of free parameters. Considerable changes are observed in the optical solitons amplitude from the results presented in the current study.

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

Similar content being viewed by others

References

  • Akinyemi, L., Nisar, K.S., Saleel, C.A., Rezazadeh, H., Veeresha, P., Khater, M.M.A., Inc, M.: Novel approach to the analysis of fifth-order weakly nonlocal fractional Schrödinger equation with Caputo derivative. Results Phys. 31, 104958 (2021a)

    Article  Google Scholar 

  • Akinyemi, L., Rezazadeh, H., Shi, Q.H., Inc, M., Khater, M.M.A., Ahmad, H., Jhangeer, A., Ali Akbar, M.: New optical solitons of perturbed nonlinear Schrödinger-Hirota equation with spatio-temporal dispersion. Results Phys. 29, 104656 (2021)

    Article  Google Scholar 

  • Ali Akbar, M., Akinyemi, L., Yao, S.W., Jhangeer, A., Rezazadeh, H., Khater, M.M.A., Ahmad, H., Inc, M.: Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method, Results Phys.25, 104228 (2021).

  • Baleanu, D., Hosseini, K., Salahshour, S., Sadri, K., Mirzazadeh, M., Park, C., Ahmadian, A.: The (2+1)-dimensional hyperbolic nonlinear Schrödinger equation and its optical solitons. AIMS Mathematics 6, 9568–9581 (2021)

    Article  MathSciNet  Google Scholar 

  • Gilson, C., Hietarinta, J., Nimmo, J., Ohta, Y.: Sasa-Satsuma higher-order nonlinear Schrödinger equation and its bilinearization and multisoliton solutions. Phys. Rev. E 68, 016614 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  • González-Gaxiola, O., Biswas, A., Ekici, M., Alshomrani, A.S.: Optical solitons with Sasa-Satsuma equation by Laplace-Adomian decomposition algorithm. Optik 229, 166262 (2021)

    Article  ADS  Google Scholar 

  • Hosseini, K., Mirzazadeh, M., Gómez-Aguilar, J.F.: Soliton solutions of the Sasa-Satsuma equation in the monomode optical fibers including the beta-derivatives. Optik 224, 165425 (2020a)

    Article  ADS  Google Scholar 

  • Hosseini, K., Mirzazadeh, M., Ilie, M., Radmehr, S.: Dynamics of optical solitons in the perturbed Gerdjikov-Ivanov equation. Optik 206, 164350 (2020b)

    Article  ADS  Google Scholar 

  • Hosseini, K., Mirzazadeh, M., Ilie, M., Gómez-Aguilar, J.F.: Biswas-Arshed equation with the beta time derivative: Optical solitons and other solutions. Optik 217, 164801 (2020c)

    Article  ADS  Google Scholar 

  • Hosseini, K., Sadri, K., Mirzazadeh, M., Chu, Y.M., Ahmadian, A., Pansera, B.A., Salahshour, S.: A high-order nonlinear Schrödinger equation with the weak non-local nonlinearity and its optical solitons. Results in Physics 23, 104035 (2021a)

    Article  Google Scholar 

  • Hosseini, K., Sadri, K., Mirzazadeh, M., Salahshour, S.: An integrable (2+1)-dimensional nonlinear Schrödinger system and its optical soliton solutions. Optik 229, 166247 (2021b)

    Article  ADS  Google Scholar 

  • Hosseini, K., Mirzazadeh, M., Baleanu, D., Raza, N., Park, C., Ahmadian, A., Salahshour, S.: The generalized complex Ginzburg-Landau model and its dark and bright soliton solutions. European Physical Journal plus 136, 709 (2021c)

    Article  ADS  Google Scholar 

  • Hosseini, K., Salahshour, S., Mirzazadeh, M.: Bright and dark solitons of a weakly nonlocal Schrödinger equation involving the parabolic law nonlinearity. Optik 227, 166042 (2021d)

    Article  ADS  Google Scholar 

  • Hosseini, K., Matinfar, M., Mirzazadeh, M.: Soliton solutions of high-order nonlinear Schrödinger equations with different laws of nonlinearities. Regular and Chaotic Dynamics 26, 105–112 (2021e)

    Article  ADS  MathSciNet  Google Scholar 

  • Khater, M.M.A., Ali Akbar, M., Akinyemi, L., Jhangeer, A., Rezazadeh, H., Inc, M.: Bifurcation of new optical solitary wave solutions for the nonlinear long-short wave interaction system via two improved models of expansion method. Opt. Quantum Electron. 53, 507 (2021)

    Article  Google Scholar 

  • Kodama, Y., Hasegawa, A.: Nonlinear pulse propagation in a monomode dielectric guide. IEEE J. Quantum Electron. 23, 510–524 (1987)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equation. Optik 206, 163550 (2020a)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations. Appl. Math. Comput. 371, 124972 (2020b)

    MathSciNet  MATH  Google Scholar 

  • Kudryashov, N.A.: Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation. Optik 206, 164335 (2020c)

    Article  ADS  Google Scholar 

  • Ma, H.C., Zhang, Z.P., Deng, A.P.: A new periodic solution to Jacobi elliptic functions of MKdV equation and BBM equation. Acta Math. Appl. Sin. 28, 409–415 (2012)

    Article  MathSciNet  Google Scholar 

  • Mirzazadeh, M., Hosseini, K., Dehingia, K., Salahshour, S.: A second-order nonlinear Schrödinger equation with weakly nonlocal and parabolic laws and its optical solitons. Optik 242, 166911 (2021)

    Article  ADS  Google Scholar 

  • Rasheed, N.M., Al-Amr, M.O., Az-Zo’bi, E.A., Tashtoush, M.A., Akinyemi, L.: Stable optical solitons for the higher-order non-Kerr NLSE via the modified simple equation method. Mathematics 9, 1986 (2021)

    Article  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Ashraf, M.A., Younis, M., Khaliq, A., Baleanu, D.: Rogue, multi-wave, homoclinic breather, M-shaped rational and periodic-kink solutions for a nonlinear model describing vibrations. Results Phys. 29, 104654 (2021)

    Article  Google Scholar 

  • Rizvi, S.T.R., Seadawy, A.R., Abbas, S.O., Latif, S., Althobaiti, S.: Exact and numerical solutions to the system of the chlorite iodide malonic acid chemical reactions. Comput. Appl. Math. 41, 13 (2022a)

    Article  MathSciNet  Google Scholar 

  • Rizvi, S.T.R., Ali, K., Bekir, A., Nawaz, B., Younis, M.: Investigation on the single and multiple dromions for nonlinear Telegraph equation in electrical transmission line. Qualitative Theory Dyn. Syst. 21, 12 (2022b)

    Article  MathSciNet  Google Scholar 

  • Seadawy, A.R., Rizvi, S.T.R., Althobaiti, S.: Chirped periodic and solitary waves for improved perturbed nonlinear Schrödinger equation with cubic quadratic nonlinearity. Fractal Fractional 5, 234 (2021)

    Article  Google Scholar 

  • Sun, F.: Optical solutions of Sasa-Satsuma equation in optical fibers. Optik 228, 166127 (2021)

    Article  ADS  Google Scholar 

  • Wazwaz, A.M., Mehanna, M.: Higher-order Sasa-Satsuma equation: Bright and dark optical solitons. Optik 243, 167421 (2021)

    Article  ADS  Google Scholar 

  • Yao, S.W., Akinyemi, L., Mirzazadeh, M., Inc, M., Hosseini, K., Şenol, M.: Dynamics of optical solitons in higher-order Sasa-Satsuma equation. Results in Physics 30, 104825 (2021)

    Article  Google Scholar 

  • Yıldırım, Y.: Optical solitons to Sasa-Satsuma model with modified simple equation approach. Optik 184, 271–276 (2019)

    Article  ADS  Google Scholar 

  • Yıldırım, Y., Biswas, A., Asma, M., Ekici, M., Triki, H., Zayed, E.M.E., Alzahrani, A.K., Belic, M.R.: Optical solitons with Sasa-Satsuma equation. Optik 219, 165183 (2020)

    Article  ADS  Google Scholar 

  • Younis, M., Ali, S., Rizvi, S.T.R., Tantawy, M., Tariq, K.U., Bekir, A.: Investigation of solitons and mixed lump wave solutions with (3+1)-dimensional potential-YTSF equation. Commun. Nonlinear Sci. Numer. Simul. 94, 105544 (2021)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

Not applicable.

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Mathematics, Islamic Azad University, Rasht Branch, Rasht, Iran

    K. Hosseini & K. Sadri

  2. Department of Mathematics, Near East University TRNC, Mersin 10, Turkey

    K. Hosseini

  3. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    S. Salahshour

  4. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey

    D. Baleanu

  5. Institute of Space Sciences, Magurele-Bucharest, Romania

    D. Baleanu

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

    M. Mirzazadeh

  7. Department of Mathematics, Firat University, Elazig, Turkey

    Mustafa Inc

  8. Department of Medical Research, China Medical University, 40447, Taichung, Taiwan

    Mustafa Inc

Authors
  1. K. Hosseini
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Sadri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Salahshour
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. Baleanu
    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. Mustafa Inc
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by KH, KS and SS. The first draft of the manuscript was written by DB, MM, MI and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Mustafa Inc.

Ethics declarations

Conflict of interest

The authors have not disclosed any competing interests.

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 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

Hosseini, K., Sadri, K., Salahshour, S. et al. The generalized Sasa–Satsuma equation and its optical solitons. Opt Quant Electron 54, 723 (2022). https://doi.org/10.1007/s11082-022-04124-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-022-04124-6

Keywords

Search

Navigation