Skip to main content
SpringerLink
Log in

Investigation of solitons and conservation laws in an inhomogeneous optical fiber through a generalized derivative nonlinear Schrödinger equation with quintic nonlinearity

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

Abstract

The current research investigates the behavior of femtosecond solitary waves in an inhomogeneous optical fiber using the generalized derivative nonlinear Schrödinger equation with quintic nonlinearity. The extended F-expansion technique is utilized to obtain various exact solutions such as bright soliton solutions, dark soliton solutions, combo bright–dark soliton solutions, singular soliton solutions, periodic solutions, Jacobi elliptic functions solutions, rational solutions, Weierstrass elliptic solutions, exponential solutions. The obtained solutions are presented in three-dimensional and contour graphics by selecting appropriate parameters. Ibragimov’s conservation technique is also applied to obtain conservation laws for the given model. These findings are crucial for comprehending various of scientific and physical 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
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

No applicable for this paper.

References

  • Abbagari, S., Houwe, A., Saliou, Y., Douvagaï, Chu, Y.-M., Inc, M., Rezazadeh, H., Doka, S.Y.: Analytical survey of the predator–prey model with fractional derivative order. AIP Adv. 11(3):035127 (2021)

  • Akbulut, A., Taşcan, F.: Lie symmetries, symmetry reductions and conservation laws of time fractional modified Korteweg–de Vries (mkdv) equation. Chaos Solitons Fract. 100, 1–6 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Akbulut, A., Taşcan, F.: Application of conservation theorem and modified extended tanh-function method to (1+1)-dimensional nonlinear coupled Klein–Gordon–Zakharov equation. Chaos Solitons Fract. 104, 33–40 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Akbulut, A., Mirzazadeh, M., Hashemi, M. S., Hosseini, K., Salahshour, S., Park, C.: Triki–Biswas model: its symmetry reduction, Nucci’s reduction and conservation laws. Int. J. Mod. Phys. B 37(07), 2350063 (2023)

  • Amiranashvili, S., Bandelow, U., Akhmediev, N.: Ultrashort optical solitons in transparent nonlinear media with arbitrary dispersion. Opt. Quant. Electron. 46(10), 1233–1238 (2014)

    Article  Google Scholar 

  • Apriliani, V., Maulidi, I., Azhari, B.: Extended F-expansion method for solving the modified Korteweg–de Vries (mkdv) equation. Al-Jabar: Jurnal Pendidikan Matematika 11(1), 93–100 (2020)

  • Chen, Y., Yan, Z.: The weierstrass elliptic function expansion method and its applications in nonlinear wave equations. Chaos Solitons Fract. 29(4), 948–964 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Chu, Y., Shallal, M.A., Mirhosseini-Alizamini, S.M., Rezazadeh, H., Javeed, S., Baleanu, D.: Application of modified extended tanh technique for solving complex Ginzburg–Landau equation considering Kerr law nonlinearity. Comput. Mater. Continua 66(2), 1369–1378 (2021)

    Article  Google Scholar 

  • Djoptoussia, C., Tiofack, C.G.L., Mohamadou, A., Kofané, T.C.: Ultrashort self-similar periodic waves and similaritons in an inhomogeneous optical medium with an external source and modulated coefficients. Nonlinear Dyn. 107(4), 3833–3846 (2022)

    Article  Google Scholar 

  • Dong, X., Xu, M., Pang, L.: Ultrashort optical pulse repetition rate multiplication based on two-core-fiber Mach–Zehnder interferometer. Opt. Quant. Electron. 50(8), 306 (2018)

    Article  Google Scholar 

  • Gagnon, L., Winternitz, P.: Symmetry classes of variable coefficient nonlinear Schrödinger equations. J. Phys. A: Math. Gen. 26(23), 7061 (1993)

    Article  ADS  MATH  Google Scholar 

  • Gao, X.-Y., Guo, Y.-J., Shan, W.-R.: Bilinear forms through the binary Bell polynomials, N solitons and Bäcklund transformations of the Boussinesq–Burgers system for the shallow water waves in a lake or near an ocean beach. Commun. Theor. Phys. 72(9), 095002 (2020)

    Article  ADS  MATH  Google Scholar 

  • Gao, X.-Y., Guo, Y.-J., Shan, W.-R.: Optical waves/modes in a multicomponent inhomogeneous optical fiber via a three-coupled variable-coefficient nonlinear Schrödinger system. Appl. Math. Lett. 120, 107161 (2021)

    Article  MATH  Google Scholar 

  • Hashemi, M.S., Baleanu, D.: Lie Symmetry Analysis of Fractional Differential Equations. Chapman and Hall/CRC (2020)

  • Ibragimov, N.H.: A new conservation theorem. J. Math. Anal. Appl. 333(1), 311–328 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  • Ibragimov, N., Khamitova, R., Avdonina, E., Galiakberova, L.: Conservation laws and solutions of a quantum drift-diffusion model for semiconductors. Int. J. Non-Linear Mech. 77, 69–73 (2015)

    Article  ADS  MATH  Google Scholar 

  • Kadkhoda, N., Lashkarian, E., Inc, M., Akinlar, M.A., Chu, Y.-M.: New exact solutions and conservation laws to the fractional-order Fokker–Planck equations. Symmetry 12(8), 1282 (2020)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: General solution of the traveling wave reduction for the perturbed Chen–Lee–Liu equation. Optik 186, 339–349 (2019)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Model of propagation pulses in an optical fiber with a new law of refractive indices. Optik 248, 168160 (2021)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Stationary solitons of the generalized nonlinear Schrödinger equation with nonlinear dispersion and arbitrary refractive index. Appl. Math. Lett. 128, 107888 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  • Mecelti, A., Triki, H., Azzouzi, F., Wei, X., Biswas, A., Yıldırım, Y., Alshehri, H.M., Zhou, Q.: New chirped gray and kink self-similar waves in presence of quintic nonlinearity and self-steepening effect. Phys. Lett. A 437, 128104 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  • Muniyappan, A., Priya, O.A., Amirthani, S., Brintha, K., Biswas, A., Ekici, M., Dakova, A., Alshehri, H.M., Belic, M.R.: Peakon and cuspon excitations in optical fibers for eighth order nonlinear Schrödinger’s model. Optik 243, 167509 (2021)

    Article  ADS  Google Scholar 

  • Muniyappan, A., Hemamalini, D., Akila, E., Elakkiya, V., Anitha, S., Devadharshini, S., Biswas, A., Yıldırım, Y., Alshehri, H.M.: Bright solitons with anti-cubic and generalized anti-cubic nonlinearities in an optical fiber. Optik 254, 168612 (2022)

    Article  ADS  Google Scholar 

  • Naz, R., Mahomed, F.M., Mason, D.P.: Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics. Appl. Math. Comput. 205(1), 212–230 (2008)

    MathSciNet  MATH  Google Scholar 

  • Rabie, W.B., Ahmed, H.M.: Constructing new soliton solutions for Kudryashov’s quintuple self-phase modulation with dual-form of generalized nonlocal nonlinearity using extended f-expansion method. Opt. Quant. Electron. 55(3), 1–16 (2023)

    Article  Google Scholar 

  • Rizvi, S.T., Seadawy, A.R., Mustafa, B., Ali, K., Ashraf, R.: Propagation of chirped periodic and solitary waves for the coupled nonlinear Schrödinger equation in two core optical fibers with parabolic law with weak non-local nonlinearity. Opt. Quant. Electron. 54(9), 545 (2022)

    Article  Google Scholar 

  • Sahoo, S., Saha Ray, S., Abdou, M. A. M., Inc, M., Chu, Y.-M.: New soliton solutions of fractional Jaulent–Miodek system with symmetry analysis. Symmetry 12(6), 1001 (2020)

  • Samir, I., Badra, N., Ahmed, H.M., Arnous, A.H.: Optical soliton perturbation with Kudryashov’s generalized law of refractive index and generalized nonlocal laws by improved modified extended tanh method. Alex. Eng. J. 61(5), 3365–3374 (2022)

    Article  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)

    Article  ADS  Google Scholar 

  • Seadawy, A.R., Rizvi, S.T., Akram, U., Naqvi, S.K.: Optical and analytical soliton solutions to higher order non-Kerr nonlinear Schrödinger dynamical model. J. Geom. Phys. 179, 104616 (2022)

    Article  MATH  Google Scholar 

  • Wang, G., Kara, A.H., Fakhar, K., Vega-Guzman, J., Biswas, A.: Group analysis, exact solutions and conservation laws of a generalized fifth order KdV equation. Chaos Solitons Fract. 86, 8–15 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Funding

No funding received for this paper.

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, Higher Institute of Engineering El Shorouk Academy, El-Shorouk City, Cairo, Egypt

    Hamdy M. Ahmed

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

    Mohammad Mirzazadeh

  4. Department of Mathematics, Faculty of Arts and Science, Bursa Uludağ University, Bursa, Turkey

    Arzu Akbulut

  5. Department of Computer Engineering, Biruni University, Istanbul, Turkey

    Mir Sajjad Hashemi

Authors
  1. Wafaa B. Rabie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hamdy M. Ahmed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mohammad Mirzazadeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Arzu Akbulut
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Mir Sajjad Hashemi
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All authors contributed equally to this work.

Corresponding author

Correspondence to Mir Sajjad Hashemi.

Ethics declarations

Ethical approval

Not applicable.

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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, H.M., Mirzazadeh, M. et al. Investigation of solitons and conservation laws in an inhomogeneous optical fiber through a generalized derivative nonlinear Schrödinger equation with quintic nonlinearity. Opt Quant Electron 55, 825 (2023). https://doi.org/10.1007/s11082-023-05070-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-05070-7

Keywords

Search

Navigation