Skip to main content
SpringerLink
Log in

New interesting optical solutions to the quadratic–cubic Schrodinger equation by using the Kudryashov-expansion method and the updated rational sine–cosine functions

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

Abstract

The updated rational sine–cosine functions and the Kudryashov-expansion method are implemented to investigate new optical explicit solitons to the generalized nonlinear Schrodinger equation. The suggested model describes the propagation of optical-solitons through optical-fibers and nonlinear medium with quadratic–cubic Kerr-law. The behavior of the obtained Schrodinger’s solutions is investigated by studying the effect of its nonlinearity and dispersion coefficients. Finally, 2D and 3D graphics are provided to support our findings.

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

Availability of data and materials

Not applicable.

References

  • Akinyemi, L., Inc, M., Khater, M.M.A., Rezazadeh, H.: Dynamical behaviour of Chiral nonlinear Schrödinger equation. Opt. Quant. Electron. 54, 191 (2022a)

    Article  Google Scholar 

  • Akinyemi, L., Senol, M., Osman, M.S.: Analytical and approximate solutions of nonlinear Schrodinger equation with higher dimension in the anomalous dispersion regime. J. Ocean Eng. Sci. 7(2), 143–154 (2022b)

    Article  Google Scholar 

  • Alhami, R., Alquran, M.: Extracted different types of optical lumps and breathers to the new generalized stochastic potential-KdV equation via using the Cole–Hopf transformation and Hirota bilinear method. Opt. Quant. Electron. 54, 553 (2022)

    Article  Google Scholar 

  • Alquran, M.: Optical bidirectional wave-solutions to new two-mode extension of the coupled KdV–Schrodinger equations. Opt. Quant. Electron. 53, 588 (2021a)

    Article  Google Scholar 

  • Alquran, M.: Physical properties for bidirectional wave solutions to a generalized fifth-order equation with third-order time-dispersion term. Res. Phys. 28, 104577 (2021b)

    Google Scholar 

  • Alquran, M., Alhami, R.: Convex-periodic, kink-periodic, peakon-soliton and kink bidirectional wave-solutions to new established two-mode generalization of Cahn–Allen equation. Res. Phys. 34, 105257 (2022)

    Google Scholar 

  • Alquran, M., Jaradat, I.: Multiplicative of dual-waves generated upon increasing the phase velocity parameter embedded in dual-mode Schrodinger with nonlinearity Kerr laws. Nonlinear Dyn. 96, 115–121 (2019)

    Article  Google Scholar 

  • Alquran, M., Jaradat, I., Baleanu, D.: Shapes and dynamics of dual-mode Hirota–Satsuma coupled KdV equations: exact traveling wave solutions and analysis. Chin. J. Phys. 58, 49–56 (2019)

    Article  MathSciNet  Google Scholar 

  • Alquran, M., Jaradat, I., Yusuf, A., Sulaiman, T.A.: Heart-cusp and bell-shaped-cusp optical solitons for an extended two-mode version of the complex Hirota model: application in optics. Opt. Quant. Electron. 53, 26 (2021)

    Article  Google Scholar 

  • Alquran, M., Ali, M., Jadallah, H.: New topological and non-topological unidirectional-wave solutions for the modified-mixed KdV equation and bidirectional-waves solutions for the Benjamin Ono equation using recent techniques. J. Ocean Eng. Sci. 7(2), 163–169 (2022)

    Article  Google Scholar 

  • Biswas, A., Ullah, M.Z., Asma, M., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical solitons with quadratic–cubic nonlinearity by semi-inverse variational principle. Optik 139, 16–19 (2017)

    Article  ADS  Google Scholar 

  • Cinar, M., Onder, I., Secer, A., Yusuf, A., Sulaiman, T.A., Bayram, M., Aydin, H.: The analytical solutions of Zoomeron equation via extended rational sin–cos and sinh–cosh methods. Phys. Scr. 96, 094002 (2021)

    Article  ADS  Google Scholar 

  • Feng, D., Jiao, J., Jiang, G.: Optical solitons and periodic solutions of the \((2+1)\)-dimensional nonlinear Schrodinger’s equation. Phys. Lett. A 382(32), 2081–2084 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  • Fujioka, J., Cortes, E., Perez-Pascual, R., Rodríguez, R.F., Espinosa, A., Malomed, B.A.: Chaotic solitons in the quadratic–cubic nonlinear Schrodinger equation under nonlinearity management. Chaos 21, 033120 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  • Jaradat, I., Alquran, M.: Geometric perspectives of the two-mode upgrade of a generalized Fisher–Burgers equation that governs the propagation of two simultaneously moving waves. J. Comput. Appl. Math. 404, 113908 (2022)

    Article  MathSciNet  Google Scholar 

  • Jaradat, I., Alquran, M., Ali, M.: A numerical study on weak-dissipative two-mode perturbed Burgers’ and Ostrovsky models: right-left moving waves. Eur. Phys. J. Plus 133, 164 (2018a)

    Article  Google Scholar 

  • Jaradat, I., Alquran, M., Momani, S., Biswas, A.: Dark and singular optical solutions with dual-mode nonlinear Schrödinger’s equation and Kerr-law nonlinearity. Optik 172, 822–825 (2018b)

    Article  ADS  Google Scholar 

  • Jhangeer, A., Muddassar, M., Inc, M., Kousar, M., Chu, Y.M.: Computation of complex fields of perturbed \((2+1)\)-dimensional Schrodinger’s hyperbolic equation. Opt. Quant. Electron. 53, 352 (2021)

    Article  Google Scholar 

  • Khuri, S.A., Wazwaz, A.M.: Soliton solutions through optical fibers for quadratic–cubic nonlinear medium: a complex Ansatze approach. Optik 229, 166268 (2021)

    Article  ADS  Google Scholar 

  • Li, B.Q., Guan, W.Y.: Symmetry breaking breathers and their phase transitions in a coupled optical fiber system. Opt. Quant. Electron. 53, 216 (2021)

    Article  Google Scholar 

  • Ma, Y.L.: Interaction and energy transition between the breather and rogue wave for a generalized nonlinear Schrodinger system with two higher-order dispersion operators in optical fibers. Nonlinear Dyn. 97, 95–105 (2019)

    Article  Google Scholar 

  • Mahak, N., Akram, G.: Exact solitary wave solutions by extended rational sine–cosine and extended rational sinh–cosh techniques. Phys. Scr. 94, 115212 (2019a)

    Article  ADS  Google Scholar 

  • Mahak, N., Akram, G.: Extension of rational sine-cosine and rational sinh–cosh techniques to extract solutions for the perturbed NLSE with Kerr law nonlinearity. Eur. Phys. J. Plus 134, 159 (2019b)

    Article  Google Scholar 

  • Mathanaranjan, T., Kumar, D., Rezazadeh, H., Akinyemi, L.: Optical solitons in metamaterials with third and fourth order dispersions. Opt. Quant. Electron. 54, 271 (2022)

    Article  Google Scholar 

  • Mirzazadeh, M., Ekici, M., Zhou, Q., Biswas, A.: Exact solitons to generalized resonant dispersive nonlinear Schrodinger’s equation with power law nonlinearity. Optik 130, 178–183 (2017)

    Article  ADS  Google Scholar 

  • Ntiamoah, D., Ofori-Atta, W., Akinyemi, L.: The higher-order modified Korteweg–de Vries equation: its soliton, breather and approximate solutions. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.06.042

    Article  Google Scholar 

  • Seadawy, A.R., Lu, D.: Bright and dark solitary wave soliton solutions for the generalized higher order nonlinear Schrödinger equation and its stability. Res. Phys. 7, 43–48 (2017)

    Google Scholar 

  • Sulaiman, T.A., Yusuf, A., Alquran, M.: Dynamics of optical solitons and nonautonomous complex wave solutions to the nonlinear Schrodinger equation with variable coefficients. Nonlinear Dyn. 104, 639–648 (2021)

    Article  Google Scholar 

Download references

Funding

No funding is received for this work.

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, 22110, Jordan

    Marwan Alquran

Authors
  1. Marwan Alquran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marwan Alquran.

Ethics declarations

Ethical approval

Not applicable.

Conflict of interest

The author declares that he has 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 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

Alquran, M. New interesting optical solutions to the quadratic–cubic Schrodinger equation by using the Kudryashov-expansion method and the updated rational sine–cosine functions. Opt Quant Electron 54, 666 (2022). https://doi.org/10.1007/s11082-022-04070-3

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-022-04070-3

Keywords

Mathematics Subject Classification

Search

Navigation