Skip to main content
SpringerLink
Log in

Optical solitons for the concatenation model with multiplicative white noise

  • Research Article
  • Published:
Journal of Optics Aims and scope Submit manuscript

Abstract

The examination of the concatenation model with spatio-temporal dispersion, Kerr law nonlinearity, and several Hamiltonian perturbation terms, in addition to the influence of multiplicative white noise, is the subject of this paper. The application of two integration approaches allows us the solutions of the model, revealing a comprehensive set of 1-soliton solutions. The enhanced Kudryashov’s mechanism and the Weistrass’ type Riccati’s projective equation approach are the two approaches utilized in this research. Soliton solutions with a unique set of parameter values are obtained through the utilization of Weierstrass elliptic functions, which are derived via the Weistrass’ type Riccati’s projective equation approach.

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

Similar content being viewed by others

References

  1. A. Ankiewicz, N. Akhmediev, Higher-order integrable evolution equation and its soliton solutions. Phys. Lett. A 378, 358–361 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. A. Ankiewicz, Y. Wang, S. Wabnitz, N. Akhmediev, Extended nonlinear Schrödinger equation with higher-order odd and even terms and its rogue wave solutions. Phys. Rev. E 89, 012907 (2014)

    Article  ADS  Google Scholar 

  3. A. Biswas, J. Vega–Guzman, A.H. Kara, S. Khan, H. Triki, O. Gonzalez–Gaxiola, L. Moraru, P.L. Georgescu, Optical solitons and conservation laws for the concatenation model: undetermined coefficients and multipliers approach. Universe 9(1), 15 (2023)

    Article  ADS  Google Scholar 

  4. Y. Yildirim, A. Biswas, L. Moraru, A.A. Alghamdi, Quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion. Mathematics 11(7), 1709 (2023)

    Article  Google Scholar 

  5. A. Biswas, J. Vega-Guzman, Y. Yildirim, L. Moraru, C. Iticescu, A.A. Alghamdi, Optical solitons for the concatenation model with differential group delay: undetermined coefficients. Mathematics 11(9), 2012 (2023)

    Article  Google Scholar 

  6. M.Y. Wang, A. Biswas, Y. Yildirim, L. Moraru, S. Moldovanu, H.M. Alshehri, Optical solitons for a concatenated model by trial equation approach. Electronics 12(1), 19 (2023)

    Article  Google Scholar 

  7. N.A. Kudryashov, A. Biswas, A.G. Borodina, Y. Yildirim, H. Alshehri, Painleve analysis and optical solitons for a concatenated model. Optik 272, 170255 (2023)

    Article  ADS  Google Scholar 

  8. A. Kukkar, S. Malik, A. Biswas, Y. Yildirim, S.P. Moshokoa, S. Khan, A.A. Alghamdi, Optical soliton for the concatenation model with Kudryashoiv’s approaches. Submitted

  9. M. Bayram, Optical bullets with Biswas–Milovic equation having Kerr and parabolic laws of nonlinearity. Optik 270, 170046 (2022)

    Article  ADS  Google Scholar 

  10. T.L. Belyaeva, M.A. Agüero, V.N. Serkin, Nonautonomous solitons of the novel nonlinear Schrödinger equation: self-compression, amplification, and the bound state decay in external potentials. Optik 244, 167584 (2021)

    Article  ADS  Google Scholar 

  11. N.A. Kudryashov, Embedded solitons of the generalized nonlinear Schrödinger equation with high dispersion. Regul. Chaotic Dyn. 27(6), 680–696 (2022)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. B.A. Malomed, New findings for the old problem: exact solutions for domain walls in coupled real Ginzburg–Landau equations. Phys. Lett. A 422, 127802 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  13. B.A. Malomed, Multidimensional dissipative solitons and solitary vortices. Chaos Solitons Fract. 163, 112526 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  14. V.N. Serkin, A. Ramirez, T.L. Belyaeva, Nonlinear-optical analogies to the Moses sea parting effect: dark soliton in forbidden dispersion or nonlinearity. Optik 192, 162928 (2019)

    Article  ADS  Google Scholar 

  15. N. Sirendaoreji, A method for constructing Weierstrass elliptic function solutions and their degenerated solutions of the mKdV equation (2022). arXiv:2210.03302v1 [nlin.SI]

  16. L. Tang, Phase portraits and multiple optical solitons perturbation in optical fibers with the nonlinear Fokas–Lenells equation. J. Opt. (2023)

  17. M.Y. Wang, Optical solitons of the perturbed nonlinear Schrödinger equation in Kerr media. Optik 243, 167382 (2021)

    Article  ADS  Google Scholar 

  18. M.Y. Wang, Highly dispersive optical solitons of perturbed nonlinear Schrödinger equation with Kudryashov’s sextic-power law nonlinear. Optik 267, 169631 (2022)

    Article  ADS  Google Scholar 

  19. M.Y. Wang, Optical solitons with perturbed complex Ginzburg–Landau equation in Kerr and cubic–quintic–septic nonlinearity. Results Phys. 33, 105077 (2022)

    Article  Google Scholar 

  20. T.Y. Wang, Q. Zhou, W.J. Liu, Soliton fusion and fission for the high-order coupled nonlinear Schrödinger system in fiber lasers. Chin. Phys. B 31, 020501 (2022)

    Article  ADS  Google Scholar 

  21. A. Secer, Stochastic optical solitons with multiplicative white noise via Itô calculus. Optik 268, 169831 (2022)

    Article  ADS  Google Scholar 

  22. H. Wang, Q. Zhou, W. Liu, Exact analysis and elastic interaction of multi-soliton for a two-dimensional Gross–Pitaevskii equation in the Bose-Einstein condensation. J. Adv. Res. 38, 179–190 (2022)

    Article  Google Scholar 

  23. A.M. Wazwaz, Bright and dark optical solitons for (3+1)-dimensional Schrödinger equation with cubic–quintic–septic nonlinearities. Optik 225, 165752 (2021)

    Article  ADS  Google Scholar 

  24. A.M. Wazwaz, Bright and dark optical solitons of the (2+1)-dimensional perturbed nonlinear Schrödinger equation in nonlinear optical fibers. Optik 251, 168334 (2022)

    Article  ADS  Google Scholar 

  25. Y. Zhong, H. Triki, Q. Zhou, Analytical and numerical study of chirped optical solitons in a spatially inhomogeneous polynomial law fiber with parity-time symmetry potential. Commun. Theor. Phys. 75, 025003 (2023)

    Article  ADS  MathSciNet  Google Scholar 

  26. Q. Zhou, D. Kumar, M. Mirzazadeh, M. Eslami, H. Rezazadeh, Optical soliton in nonlocal nonlinear medium with cubic-quintic nonlinearities and spatio-temporal dispersion. Acta Phys. Pol., A 134(6), 1204–1210 (2018)

    Article  ADS  Google Scholar 

  27. Q. Zhou, H. Rezazadeh, A. Korkmaz, M. Eslami, M. Mirzazadeh, M. Rezazadeh, New optical solitary waves for unstable Schrödinger equation in nonlinear medium. Opt. Appl. 49(1), 135–150 (2019)

    Google Scholar 

  28. Q. Zhou, Influence of parameters of optical fibers on optical soliton interactions. Chin. Phys. Lett. 39(1), 010501 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  29. Q. Zhou, Y. Sun, H. Triki, Y. Zhong, Z. Zeng, M. Mirzazadeh, Study on propagation properties of one-soliton in a multimode fiber with higher-order effects. Results Phys. 41, 105898 (2022)

    Article  Google Scholar 

  30. Q. Zhou, Z. Luan, Z. Zeng, Y. Zhong, Effective amplification of optical solitons in high power transmission systems. Nonlinear Dyn. 109(4), 3083–3089 (2022)

    Article  Google Scholar 

  31. R.K. Dowluru, P.R. Bhima, Influences of third-order dispersion on linear birefringent optical soliton transmission systems. J. Opt. 40, 132–142 (2011)

    Article  Google Scholar 

  32. S. Nandy, V. Lakshminarayanan, Adomian decomposition of scalar and coupled nonlinear Schrödinger equations and dark and bright solitary wave solutions. J. Opt. 44, 397–404 (2015)

    Article  Google Scholar 

  33. S.L. Xu, N. Petrović, M.R. Belić, Two-dimensional dark solitons in diffusive nonlocal nonlinear media. J. Opt. 44, 172–177 (2015)

    Article  Google Scholar 

  34. L. Tang, Bifurcations and optical solitons for the coupled nonlinear Schrödinger equation in optical fiber Bragg gratings. J. Opt. (2022). https://doi.org/10.1007/s12596-022-00963-4

    Article  Google Scholar 

  35. H. Vahed, Freezing of the moving cavity soliton in an array of cavity solitons. J. Opt. 46, 342–346 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt

    Elsayed M. E. Zayed

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

    Ahmed H. Arnous

  3. Department of Mathematics and Physics, Grambling State University, Grambling, LA, 71245, USA

    Anjan Biswas

  4. Mathematical Modeling and Applied Computation (MMAC) Research Group Center of Modern Mathematical Sciences and their Applications (CMMSA), Department of Mathematics, King Abdulaziz University, 21589, Jeddah, Saudi Arabia

    Anjan Biswas & Asim Asiri

  5. Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, 800201, Galaţi, Romania

    Anjan Biswas

  6. Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, Pretoria, 0204, South Africa

    Anjan Biswas

  7. Department of Computer Engineering, Biruni University, 34010, Istanbul, Turkey

    Yakup Yıldırım

  8. Department of Mathematics, Near East University, 99138, Nicosia, Cyprus

    Yakup Yıldırım

Authors
  1. Elsayed M. E. Zayed
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ahmed H. Arnous
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anjan Biswas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yakup Yıldırım
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Asim Asiri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anjan Biswas.

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

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12596-023-01381-w

Keywords

OCIS Codes

Search

Navigation