Skip to main content
SpringerLink
Log in

Optical soliton solutions of stochastic Schrödinger–Hirota equation in birefringent fibers with spatiotemporal dispersion and parabolic law nonlinearity

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

Abstract

In this paper, the stochastic Schrödinger–Hirota equation with spatiotemporal dispersion and parabolic law nonlinearity is studied from the field of nonlinear optics, which is usually used to describe the optical soliton propagation in birefringent fibers. Firstly, the stochastic Schrödinger–Hirota equation is converted into nonlinear ordinary differential equation by using the traveling wave transformation. Secondly, the optical soliton solutions of the stochastic Schrödinger–Hirota equation are obtained by using the complete discriminant system method. Finally, three-dimensional, two-dimensional, and contour maps of optical soliton solutions of the stochastic Schrödinger–Hirota equation are drawn by using the Maple 2022 software. The optical soliton solutions obtained in this article can further help researchers understand the propagation of optical solitons in birefringent fibers.

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

Data availability

No data were used for the research described in the article.

References

  1. E.M.E. Zayed, R.M.A. Shohib, A. Biswas et al., Optical solitons and conservation laws associated with Kudryashov’s sextic power-law nonlinearity of refractive index. Ukr. J. Phys. Opt. 22, 38 (2021)

    Article  Google Scholar 

  2. A.R. Adem, B. Ntsime, A. Biswas et al., Stationary optical solitons with nonlinear chromatic dispersion for Lakshmanan–Porsezian–Daniel model having Kerr law of nonlinear refractive index. Ukr. J. Phys. Opt. 22, 83 (2021)

    Article  Google Scholar 

  3. A. Biswas, J. Edoki, P. Guggilla et al., Cubic-quartic optical solitons in Lakshmanan–Porsezian–Daniel model derived with semi-inverse variational principle. Ukr. J. Phys. Opt. 22, 123 (2021)

    Article  Google Scholar 

  4. Y. Yıldırım, A. Biswas, P. Guggilla et al., Optical solitons in fibre Bragg gratings with third- and fourth-order dispersive reflectivities. Ukr. J. Phys. Opt. 22, 239 (2021)

    Article  Google Scholar 

  5. Y. Yıldırım, A. Biswas, A. Dakova et al., Cubic-quartic optical solitons having quadratic-cubic nonlinearity by sine-Gordon equation approach. Ukr. J. Phys. Opt. 22, 255 (2021)

    Article  Google Scholar 

  6. E.M.E. Zayed, R. Shohib, M. Alngar et al., Optical solitons in the Sasa-Satsuma model with multiplicative noise via Itô calculus. Ukr. J. Phys. Opt. 23, 9 (2022)

    Article  Google Scholar 

  7. Y. Yıldırım, A. Biswas, S. Khan et al., Highly dispersive optical soliton perturbation with Kudryashov’s sextic-power law of nonlinear refractive index. Ukr. J. Phys. Opt. 23, 24 (2022)

    Article  Google Scholar 

  8. O. González-Gaxiola, A. Biswas, Y. Yıldırım et al., Highly dispersive optical solitons in birefringent fibres with non-local form of nonlinear refractive index: Laplace-Adomian decomposition. Ukr. J. Phys. Opt. 23, 68 (2022)

    Article  Google Scholar 

  9. A.A. Al Qarni, A.M. Bodaqah, A.S.H.F. Mohammed et al., Cubic-quartic optical solitons for Lakshmanan–Porsezian–Daniel equation by the improved Adomian decomposition scheme. Ukr. J. Phys. Opt. 23, 228 (2022)

    Article  Google Scholar 

  10. A.A. Al Qarni, A.M. Bodaqah, A.S.H.F. Mohammed et al., Dark and singular cubic-quartic optical solitons with Lakshmanan–Porsezian–Daniel equation by the improved adomian decomposition scheme. Ukr. J. Phys. Opt. 24, 46 (2023)

    Article  Google Scholar 

  11. A. Kukkar, S. Kumar, S. Malik et al., Optical solitons for the concatenation model with Kurdryashov’s approaches. Ukr. J. Phys. Opt. 24, 155 (2023)

    Article  Google Scholar 

  12. A. Biswas, J. Vega-Guzman, Y. Yıldırım et al., Optical solitons for the concatenation model with power-law nonlinearity: undetermined coefficients. Ukr. J. Phys. Opt. 24, 185 (2023)

    Article  Google Scholar 

  13. E.M.E. Zayed, M.E.M. Alngar, A. Biswas et al., Optical solitons in fiber Bragg gratings with quadratic-cubic law of nonlinear refractive index and cubic-quartic dispersive reflectivity. Proc. Estonian Acad. Sci. 71, 165 (2022)

    Article  MathSciNet  Google Scholar 

  14. O. González-Gaxiola, A. Biswas, Y. Yıldırım et al., Optical solitons in fiber Bragg gratings with quadratic-cubic law of nonlinear refractive index and cubic-quartic dispersive reflectivity. Proc. Estonian Acad. Sci. 71, 213 (2022)

    Article  MathSciNet  Google Scholar 

  15. Y. Yıldırım, A. Biswas, A.H. Kara et al., Optical soliton perturbation and conservation law with Kudryashov’s refractive index having quadrupled power-law and dual form of generalized nonlocal nonlinearity. Semicond. Phys. Quantum Electron. Optoelectron. 24, 64 (2021)

    Article  Google Scholar 

  16. Y. Yıldırım, A. Biswas, S. Khan et al., Embedded solitons with \(\chi ^{2}\) and \(\chi ^{3}\) nonlinear susceptibilities. Semicond. Phys. Quantum Electron. Optoelectron. 24, 160 (2021)

    Article  Google Scholar 

  17. A. Biswas, A. Dakova, S. Khan et al., Cubic-quartic optical soliton perturbation with Fokas–Lenells equation by semi-inverse variation. Semicond. Phys. Quantum Electron. Optoelectron. 24, 431 (2021)

    Article  Google Scholar 

  18. M.M.A. Khater, Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect. Int. J. Mod. Phys. B 37, 2350083 (2023)

    Article  ADS  Google Scholar 

  19. A. Biswas, D. Milovic, M. Edwards, Mathematical Theory of Dispersion-Managed Optical Solitons (Springer, Berlin, 2010)

    Book  Google Scholar 

  20. S. Tarla, K.K. Ali, R. Yilmazer et al., New optical solitons based on the perturbed Chen-Lee-Liu model through Jacobi elliptic function method. Opt. Quant. Electron. 54, 131 (2022)

    Article  Google Scholar 

  21. Z. Li, C. Huang, Bifurcation, phase portrait, chaotic pattern and optical soliton solutions of the conformable Fokas–Lenells model in optical fibers. Chaos Solitons Fractals 169, 113237 (2023)

    Article  MathSciNet  Google Scholar 

  22. N. Raza, M.H. Rafiq, A. Bekir et al., Optical solitons related to (2+1)-dimensional Kundu-Mukherjee-Naskar model using an innovative integration architecture. J. Nonlinear Opt. Phys. Mater. 31, 2250014 (2022)

    Article  ADS  Google Scholar 

  23. M.M. Haque, M.A. Akbar, M.S. Osman, Optical soliton solutions to the fractional nonlinear Fokas–Lenells and paraxial Schrödinger equations. Opt. Quantum Electron. 54, 764 (2022)

    Article  Google Scholar 

  24. Z. Li, C. Huang, B. Wang, Phase portrait, bifurcation, chaotic pattern and optical soliton solutions of the Fokas–Lenells equation with cubic-quartic dispersion in optical fibers. Phys. Lett. A 465, 128714 (2023)

    Article  MathSciNet  Google Scholar 

  25. L. Tang, Bifurcations analysis and multiple solitons in birefringent fibers with coupled Schrödinger–Hirota equation. Chaos Solitons Fractals 161, 112383 (2022)

    Article  Google Scholar 

  26. Y. Alhojilan, H.M. Ahmed, Novel analytical solutions of stochastic Ginzburg–Landau equation driven by Wiener process via the improved modified extended tanh function method. Alex. Eng. J. 72, 269–274 (2023)

    Article  Google Scholar 

  27. T.A. Khalil, N. Badra, H.M. Ahmed et al., Optical solitons and other solutions for coupled system of nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index by Jacobi elliptic function expansion method. Optik 253, 168540 (2022)

    Article  ADS  Google Scholar 

  28. A.R. Seadawy, H.M. Ahmed, W.B. Rabie et al., An alternate pathway to solitons in magneto-optic waveguides with triple-power law nonlinearity. Optik. 231, 166840 (2021)

    Article  Google Scholar 

  29. M. Ahmed, A. Zaghrout, H.M. Ahmed, Construction of solitons and other solutions for NLSE with Kudryashov’s generalized nonlinear refractive index. Alex. Eng. J. 64, 391 (2023)

    Article  Google Scholar 

  30. Y. Alhojilan, H.M. Ahmed, W.B. Rabie, Stochastic solitons in birefringent fibers for Biswas–Arshed equation with multiplicative white noise via Itô calculus by modified extended mapping method. Symmetry. 15, 207 (2023)

    Article  ADS  Google Scholar 

  31. M.M.A. Khater, S.H. Alfalqi, J.F. Alzaidi et al., Novel soliton wave solutions of a special model of the nonlinear Schrödinger equations with mixed derivatives. Results Phys. 47, 106367 (2023)

    Article  Google Scholar 

  32. H. Rezazadeh, A.G. Davodi, D. Gholami, Combined formal periodic wave-like and soliton-like solutions of the conformable Schrödinger-KdV equation using the \((G^{\prime }/G)\)-expansion technique. Results Phys. 47, 106352 (2023)

    Article  Google Scholar 

  33. L. Tang, Phase characterization and optical solitons for the stochastic nonlinear Schrödinger equation with multiplicative white noise and spatio-temporal dispersion via Itô calculus. Optik 279, 170748 (2023)

    Article  ADS  Google Scholar 

  34. N.A. Kudryashov, Optical solitons of the Schrödinger–Hirota equation of the fourth order. Optik 274, 170587 (2023)

    Article  ADS  Google Scholar 

  35. Z. Li, Bifurcation and traveling wave solution to fractional Biswas–Arshed equation with the beta time derivative. Chaos Solitons Fractals 160, 112249 (2022)

    Article  MathSciNet  Google Scholar 

  36. H. Cakicioglu, M. Cinar, A. Secer et al., Optical solitons for Kundu–Mukherjee–Naskar equation via enhanced modified extended tanh method. Opt. Quant. Electron. 55, 400 (2023)

    Article  Google Scholar 

  37. K.Q. Tran, D.H. Nguyen, Exponential stability of impulsive stochastic differential equations with Markovian switching. Syst. Control Lett. 162, 105178 (2022)

    Article  MathSciNet  Google Scholar 

  38. Q. Zhu, \(p\)th moment exponential stability of impulsive stochastic functional differential equations with Markovian switching. J. Franklin Inst. 351(7), 3965–3986 (2014)

    Article  MathSciNet  Google Scholar 

  39. M.M.A. Khater, Novel computational simulation of the propagation of pulses in optical fibers regarding the dispersion effect. Int. J. Mod. Phys. B 37, 2350083 (2023)

    Article  ADS  Google Scholar 

  40. M.M.A. Khater, A hybrid analytical and numerical analysis of ultra-short pulse phase shifts. Chaos Solitons Fractals 169, 113232 (2023)

    Article  MathSciNet  Google Scholar 

  41. M.M.A. Khater, S.H. Alfalqi, J.F. Alzaidi et al., Analytically and numerically, dispersive, weakly nonlinear wave packets are presented in a quasi-monochromatic medium. Results Phys. 46, 106312 (2023)

    Article  Google Scholar 

  42. M.M.A. Khater, Prorogation of waves in shallow water through unidirectional Dullin–Gottwald–Holm model; computational simulations. Int. J. Mod. Phys. B 37, 2350071 (2023)

    Article  ADS  Google Scholar 

  43. M.M.A. Khater, In solid physics equations, accurate and novel soliton wave structures for heating a single crystal of sodium fluoride. Int. J. Mod. Phys. B. 37, 2350068 (2023)

    Article  ADS  Google Scholar 

  44. M.M.A. Khater, Nonlinear elastic circular rod with lateral inertia and finite radius: dynamical attributive of longitudinal oscillation. Int. J. Mod. Phys. B 37, 2350052 (2023)

    Article  ADS  Google Scholar 

  45. M.M.A. Khater, X. Zhang, R.A.M. Attia, Accurate computational simulations of perturbed Chen–Lee–Liu equation. Results Phys. 45, 106227 (2023)

    Article  Google Scholar 

  46. M.M.A. Khater, Multi-vector with nonlocal and non-singular kernel ultrashort optical solitons pulses waves in birefringent fibers. Chaos Solitons Fractals 167, 113098 (2023)

    Article  MathSciNet  Google Scholar 

  47. M.M.A. Khater, Physics of crystal lattices and plasma; analytical and numerical simulations of the Gilson-Pickering equation. Results Phys. 44, 106193 (2023)

    Article  Google Scholar 

  48. R.A.M. Attia, X. Zhang, M.M.A. Khater, Analytical and hybrid numerical simulations for the (2+1)-dimensional Heisenberg ferromagnetic spin chain. Results Phys. 43, 106045 (2023)

    Article  Google Scholar 

  49. T. Han, Z. Li, K. Zhang, Exact solutions of the stochastic fractional long-short wave interaction system with multiplicative noise in generalized elastic medium. Results Phys. 44, 106174 (2022)

    Article  Google Scholar 

  50. W.W. Mohammed, N. lqbal, A.M. Albalahi et al., Brownian motion effects on analytical solutions of a fractional-space long-short-wave interaction with conformable derivative. Results Phys. 35, 105371 (2022)

  51. M. Mouy, H. Boulares, S. Alshammari et al., On averaging principle for Caputo–Hadamard fractional stochastic differential pantograph equation. Fractal Fract. 7, 31 (2023)

    Article  Google Scholar 

  52. E.M.E. Zayed, R.M.A. Shohib, M.E.M. Alngar, Dispersive optical solitons in birefringent fibers for stochastic Schrödinger–Hirota with parabolic law nonlinearity and spatiotemporal dispersion having multiplicative white noise. Optik 278, 170736 (2022)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Computer Science, Chengdu University, Chengdu, 610106, People’s Republic of China

    Zhao Li & Enmin Zhu

Authors
  1. Zhao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Enmin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhao Li.

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

Li, Z., Zhu, E. Optical soliton solutions of stochastic Schrödinger–Hirota equation in birefringent fibers with spatiotemporal dispersion and parabolic law nonlinearity. J Opt 53, 1302–1308 (2024). https://doi.org/10.1007/s12596-023-01287-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12596-023-01287-7

Keywords

Search

Navigation