Skip to main content
SpringerLink
Log in

Dynamics of novel exact soliton solutions of concatenation model using effective techniques

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

Abstract

The exact soliton solutions of concatenated model are extracted in this research paper. Two exact methods, \(\exp (-s(\Lambda ))\)-expansion method and extended \((\frac{G'}{G^{2}})\)-expansion method, are applied to extract soliton solution of concatenated model. The proposed model is concatenation of Lakshmanan-Porsezian-Daniel equation, Sasa-Satsuma equation and nonlinear Schrödinger’s equation. Many novel solutions of concatenated model such as periodic wave, bright soliton, bright-dark soliton, dark soliton, kink soliton and many other singular soliton solutions are retrieved using proposed methods. The retrieved soliton solutions play a significant role in nonlinear physics, optical fibers and quantum mechanics. In order to display the retrieved soliton solutions graphically, 2D line graphs, contour graphs and 3D graphs have been utilized.

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

Similar content being viewed by others

Data availability

No data associated with this manuscript.

References

  • Akram, G., Sadaf, M., Khan, M.A.U.: Soliton solutions of Lakshmanan-Porsezian-Daniel model using modified auxiliary equation method with parabolic and anti-cubic law of nonlinearities. Optik 252, 1–18 (2022)

    Article  ADS  Google Scholar 

  • Akram, G., Sadaf, M., Khan, M.A.U., Pamiri, S.: Dynamic investigation of the Laksmanan-Porsezian-Daniel model with Kerr, parabolic, and anti-cubic laws of nonlinearities. Front. Phys. 10, 1–14 (2022)

    Article  Google Scholar 

  • Akram, G., Sadaf, M., Khan, M.A.U.: Soliton dynamics of the generalized shallow water like equation in nonlinear phenomenon. Front. Phys. 10, 1–8 (2022)

    Article  Google Scholar 

  • Akram, G., Sadaf, M., Khan, M.A.U.: Soliton solutions of the resonant nonlinear Schrödinger equation using modified auxiliary equation method with three different nonlinearities. Math. Comput. Simul. 206, 1–20 (2023)

    Article  Google Scholar 

  • Alquran, M., Jaradat, H.M., Syam, M.I.: Analytical solution of the time-fractional Phi-4 equation by using modified residual power series method. Nonlinear Dyn. 90, 2525–2529 (2017)

    Article  MathSciNet  Google Scholar 

  • Arnous, A.H.: Optical solitons to the cubic quartic Bragg gratings with anti-cubic nonlinearity using new approach. Optik 251, 1–8 (2022)

    Article  ADS  Google Scholar 

  • Arnous, A., Ekici, M., Moshokoa, S., Zaka Ullah, M., Biswas, A., Belic, M.: Solitons in nonlinear directional couplers with optical metamaterials by trial function scheme. Acta Phys. Pol., A 132(4), 1399–1410 (2017)

    Article  ADS  CAS  Google Scholar 

  • Arnous, A.H., Mirzazadeh, M., Akinyemi, L., Akbulut, A.: New solitary waves and exact solutions for the fifth-order nonlinear wave equation using two integration techniques. J. Ocean Eng. Sci. 8(5), 475–480 (2022)

    Article  Google Scholar 

  • Arnous, A.H., Biswas, A., Kara, A.H., Yıldırım, Y., Dragomir, C.M.B., Asiri, A.: Optical solitons and conservation laws for the concatenation model in the absence of self-phase modulation. J. Opt. (2023). https://doi.org/10.1007/s12596-023-01392-7

    Article  Google Scholar 

  • Arnous, A.H., Biswas, A., Kara, A.H., Yıldırım, Y., Moraru, L., Iticescu, C., Moldovanu, S., Alghamdi, A.A.: Optical solitons and conservation laws for the concatenation model: power-law nonlinearity. Ain Shams Eng. J. 15, 1–8 (2023)

    Article  Google Scholar 

  • Arnous, A.H., Biswas, A., Kara, A.H., Yıldırım, Y., Moraru, L., Iticescu, C., Moldovanu, S., Alghamdi, A.A.: Optical solitons and conservation laws for the concatenation model with spatio-temporal dispersion (internet traffic regulation). J. Eur. Opt. Soc.-Rapid Publ. 19(2), 1–7 (2023)

    Article  Google Scholar 

  • Arshed, S.: New soliton solutions to the perturbed nonlinear Schrödinger equation by exp(- \(\phi\) (\(\xi\)))-expansion method. Optik 220, 1–12 (2020)

    Article  ADS  Google Scholar 

  • Biswas, A., Vega-Guzman, J., Kara, A.H., Khan, S., Triki, H., González-Gaxiola, O., Moraru, L., Georgescu, P.L.: Optical solitons and conservation laws for the concatenation model: undetermined coefficients and multipliers approach. Universe 9(1), 1–10 (2022)

    Article  ADS  Google Scholar 

  • Chou, D., Ur Rehman, H., Amer, A., Aatika, A.: New solitary wave solutions of generalized fractional Tzitzéica-type evolution equations using sardar sub-equation method. Opt. Quant. Electron. 55(13), 1–16 (2023)

    Article  Google Scholar 

  • Hosseini, K., Hincal, E., Baleanu, D., Obi, O.A., Salahshour, S.: Non-singular multi-complexiton wave to a generalized KdV equation. Nonlinear Dyn. 111(8), 7591–7597 (2023)

    Article  Google Scholar 

  • Malik, S., Kumar, S., Biswas, A., Yıldırım, Y., Moraru, L., Moldovanu, S., Iticescu, C., Alshehri, H.M.: Cubic-quartic optical solitons in fiber bragg gratings with dispersive reflectivity having parabolic law of nonlinear refractive index by lie symmetry. Symmetry 14(11), 1–17 (2022)

    Article  ADS  Google Scholar 

  • Malik, S., Kumar, S., Biswas, A., Yıldırım, Y., Moraru, L., Moldovanu, S., Iticescu, C., Moshokoa, S.P., Bibicu, D., Alotaibi, A.: Gap solitons in fiber Bragg Gratings having polynomial law of nonlinear refractive index and cubic-quartic dispersive reflectivity by lie symmetry. Symmetry 15(5), 1–14 (2023)

    Article  ADS  Google Scholar 

  • Rehman, H.U., Iqbal, I., Zulfiqar, H., Gholami, D., Rezazadeh, H.: Stochastic soliton solutions of conformable nonlinear stochastic systems processed with multiplicative noise. Phys. Lett. A 486, 1–8 (2023)

    Article  MathSciNet  CAS  Google Scholar 

  • Sahoo, S., Ray, S.S., Abdou, M.A.: New exact solutions for time-fractional Kaup-Kupershmidt equation using improved (g’/g)-expansion and extended (g’/g)-expansion methods. Alex. Eng. J. 59(5), 3105–3110 (2020)

    Article  Google Scholar 

  • Samir, I., Badra, N., Ahmed, H.M., Arnous, A.H.: Solitons in birefringent fibers for CGL equation with Hamiltonian perturbations and Kerr law nonlinearity using modified extended direct algebraic method. Commun. Nonlinear Sci. Numer. Simul. 102, 1–12 (2021)

    Article  MathSciNet  Google Scholar 

  • Shahzad, M.U., Rehman, H.U., Awan, A.U., Zafar, Z., Hassan, A.M., Iqbal, I.: Analysis of the exact solutions of nonlinear coupled Drinfeld-Sokolov-Wilson equation through \(\phi\)6-model expansion method. Results Phys. 52, 1–9 (2023)

    Article  Google Scholar 

  • Shi, D., Rehman, H.U., Iqbal, I., Vivas-Cortez, M., Saleem, M.S., Zhang, X.: Analytical study of the dynamics in the double-chain model of DNA. Results Phys. 52, 1–9 (2023)

    Article  Google Scholar 

  • Sonmezoglu, A., Ekici, M., Arnous, A.H., Zhou, Q., Moshokoa, S.P., Ullah, M.Z., Biswas, A., Belic, M.: Parallel propagation of dispersive optical solitons by extended trial equation method. Optik 144, 565–572 (2017)

    Article  ADS  Google Scholar 

  • Wang, M.Y., Biswas, A., Yıldırım, Y., Moraru, L., Moldovan, S., Alshehri, H.M.: Optical solitons for a concatenation model by trial equation approach. Electronics 12(1), 1–7 (2022)

    Article  Google Scholar 

  • Yadav, R., Malik, S., Kumar, S., Sharma, R., Biswas, A., Yıldırım, Y., González-Gaxiola, O., Moraru, L., Alghamdi, A.A.: Highly dispersive W-shaped and other optical solitons with quadratic-cubic nonlinearity: symmetry analysis and new Kudryashov's method. Chaos, Solitons Fractals 173, 1–8 (2023)

    Article  MathSciNet  Google Scholar 

  • Yıldırım, Y., Biswas, A., Moraru, L., Alghamdi, A.A.: Quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion. Mathematics 11(7), 1–25 (2023)

    Article  Google Scholar 

  • Zahran, E.H.M., Bekir, A.: Optical soliton solutions to the perturbed biswas-milovic equation with kudryashov s law of refractive index. Opt. Quant. Electron. 55(14), 1–23 (2023)

    Article  Google Scholar 

  • Zahran, E.H.M., Bekir, A.: New variety diverse solitary wave solutions to the DNA Peyrard-Bishop model. Mod. Phys. Lett. B 37(13), 1–13 (2023)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  • Zainab, I., Akram, G.: Effect of \(\beta\)-derivative on time fractional Jaulent-Miodek system under modified auxiliary equation method and \(\exp (-g(\omega ))\)-expansion method. Chaos, Solitons Fractals 168, 1–10 (2023)

    Article  Google Scholar 

  • Zayed, E.M.E., Arnous, A.H., Biswas, A., Yıldırım, Y., Asiri, A.: Optical solitons for the concatenation model with multiplicative white noise. J. Opt. (2023). https://doi.org/10.1007/s12596-023-01381-w

    Article  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, 54590, Pakistan

    M. Atta Ullah Khan, Ghazala Akram & Maasoomah Sadaf

Authors
  1. M. Atta Ullah Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ghazala Akram
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maasoomah Sadaf
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

MAUK participated in the conceptualization, data curation, investigation, methodology, software implementation, visualization and writing the original draft. GA participated in the conceptualization, administration, methodology, validation, visualization and writing of the manuscript. MS participated in the formal analysis, supervision, software, data curation, review and editing of the manuscript.

Corresponding author

Correspondence to Maasoomah Sadaf.

Ethics declarations

Conflict of interest

The authors declare no 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 (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

Khan, M.A.U., Akram, G. & Sadaf, M. Dynamics of novel exact soliton solutions of concatenation model using effective techniques. Opt Quant Electron 56, 385 (2024). https://doi.org/10.1007/s11082-023-05957-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-023-05957-5

Keywords

Search

Navigation