Chirped W-shape bright, dark and other solitons solutions of a conformable fractional nonlinear Schrödinger’s equation in nonlinear optics

Abstract

In this work, two types of integration architecture, namely the sine-Gordon expansion and modified \(\exp (-\psi (\xi )\)-expansion function methods are used for constructing chirped W-shape bright, dark and other solitons solutions to perturbed nonlinear Schrödinger’s equation with conformable fractional order. The paper addresses optical solitons which are serviced in fields of nonlinear optics. As results, various types of new chirped soliton solutions and other solitons solutions not yet reported in the literature are obtained. These solutions associated with their chirp are included dark, bright optical solitons, hyperbolic, periodic and other types of solitons solutions. Moreover, some graphical representations were done successfully to stress out the virtue of the fractional order derivative.

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References

  1. [1]

    M S Osman, H Rezazadeh and E Mostafa Nonlinear Eng. 8 559 (2019)

    ADS  Article  Google Scholar 

  2. [2]

    A Javid, N Raza and M S Osman Commun. Theor. Phys. 71 362 (2019)

    ADS  Article  Google Scholar 

  3. [3]

    M S Osman Nonlinear Dyn. 96 1491 (2019)

    Article  Google Scholar 

  4. [4]

    B Ghanbari, M S Osman and D Baleanu Mod. Phys. Lett. A 34 1950155 (2019)

    ADS  Article  Google Scholar 

  5. [5]

    M S Osman, D Lu and M M A Khater Results Phys. 13 102157 (2019)

  6. [6]

    M S Osman (2017) Nonlinear Dyn. 87 1209 (2017)

    Article  Google Scholar 

  7. [7]

    S Nestor, G Betchewe, H Rezazadeh, A Bekir and S Y Doka Opt. Quant. Electron. 52 318 (2020)

    Article  Google Scholar 

  8. [8]

    S Nestor, G Betchewe, M Inc and S Y Doka Eur. Phys. J. Plus 135 380 (2020)

  9. [9]

    P A Franken, A E Hill, C W Peters and G Weinreich Phys. Rev. Lett. 7 118 (1961)

    ADS  Article  Google Scholar 

  10. [10]

    H Alphonse, A Souleymanou, M Inc, B Gambo, S Y Doka, T C Kofane and K S Nisar Results Phys. 18 103188 (2020).

    Article  Google Scholar 

  11. [11]

    H Alphonse, A Souleymanou, S Yakada, M Inc and B Dumitru Results Phys. 17 103127 (2020)

    Article  Google Scholar 

  12. [12]

    S Nestor, H Alphonse, A Souleymanou, M Inc, G Betchewe and S Y Doka Commun. Theor. Phys. 72 065501 (2020).

    ADS  Article  Google Scholar 

  13. [13]

    A A Goyal, R Gupta, C N Kumar and T S Raju Phys. Rev A 84 063810 (2011)

    Article  Google Scholar 

  14. [14]

    S Y Doka., M Justin, B Gambo and T C Kofane Nonlinear Dyn. 90 13 (2017)

    Article  Google Scholar 

  15. [15]

    H Bulut, T A Sulaiman and H M Baskonus Optik 163 49 (2018)

    ADS  Article  Google Scholar 

  16. [16]

    A Esen, T A Sulaiman, H Bulut and H M Baskonus Optik 167 150 (2018)

    ADS  Article  Google Scholar 

  17. [17]

    H Bulut, T A Sulaiman and H M Baskonus Superlattices Microstruct. 123 12 (2018)

    ADS  Article  Google Scholar 

  18. [18]

    H Bulut, T A Sulaiman, H M Baskonus, H Rezazadeh, M Eslami and M Mirzazadeh Optik 172 20 (2018)

    ADS  Article  Google Scholar 

  19. [19]

    S Nestor, H Alphonse, H Rezazadeh, A Bekir, B Gambo and S Y Doka Mod. Phys. Lett. B 34 2050246 (2020)

    ADS  Article  Google Scholar 

  20. [20]

    A Biswas et al Optik 165 233 (2018)

  21. [21]

    H Rezazadeh et al Optik 172 545 (2018).

  22. [22]

    J Sabiu, H Rezazadeh, H Tariq and A Bekir Mod. Phys. Lett. B 33 1950308 (2019)

    ADS  Article  Google Scholar 

  23. [23]

    N Raza, M R Aslam and H Rezazadeh, Opt. Quant. Electron. 51 59 (2019)

    Article  Google Scholar 

  24. [24]

    Q Zhou et al Nonlinear Dyn. 80 1365 (2015)

  25. [25]

    Q Zhou, M Mirzazadeh, M Ekici and A Sonmezoglu Nonlinear Dyn. 86 623 (2016)

    Article  Google Scholar 

  26. [26]

    S T R Rizvi and K Ali, Nonlinear Dyn. 87 1967 (2017)

    Article  Google Scholar 

  27. [27]

    Z Hammouch, T Mekkaoui and P Agarwal Eur. Phys. J. Plus 133 248 (2018)

    Article  Google Scholar 

  28. [28]

    Z Hammouch and T Mekkaoui Int. J. Appl. Math. Res. 1 206 (2012)

    Article  Google Scholar 

  29. [29]

    M S Osman Pramana 93 26 (2019)

    ADS  Article  Google Scholar 

  30. [30]

    M S Osman and W Abdul-Majid Math. Methods Appl. Sci. 42 6277 (2019)

    ADS  MathSciNet  Article  Google Scholar 

  31. [31]

    L Jian-Guo, M S Osman, Z Wen-Hui, Z Li and A Guo-Ping Appl. Phys. B 125 175 (2019)

    ADS  Google Scholar 

  32. [32]

    H Alphonse J Sabi’u, Z Hammouch and S Y Doka Phys. Scr. 95 045203 (2020)

    ADS  Article  Google Scholar 

  33. [33]

    N Savaïssou, J Mibaile, Z. Douvagai, B Gambo, S Y Doka and T C Kofane Asian-Eur. J. Math. 13 2050043 (2018)

    Google Scholar 

  34. [34]

    M Caputo Geophys J. R. Astron. Soc. 13 529 (1967)

    ADS  Article  Google Scholar 

  35. [35]

    S Nestor et al Phys. Scr. 95 085108 (2020)

  36. [36]

    A Atangana and D Baleanu, Filomat 31 2243 (2017)

    MathSciNet  Article  Google Scholar 

  37. [37

    R Khalil, M Al-Horani, A Yousef and M Sababheh J. Comput. Appl. Math. 264 65 (2014)

    MathSciNet  Article  Google Scholar 

  38. [38]

    A F Mohammed, C H Teik and S P Majumder J. Opt. Commun.21 165 (2000)

    Article  Google Scholar 

  39. [39]

    M Inc, A Yusuf, A I Aliyu and D Baleanu Opt. Quant. Electron. 50 139 (2018)

    Article  Google Scholar 

  40. [40]

    D Kumar, K Hosseini and F Samadani Optik 149 439 (2017)

    ADS  Article  Google Scholar 

  41. [41]

    C Yan Phys. Lett. A 224 77 (1996)

    ADS  MathSciNet  Article  Google Scholar 

  42. [42]

    H Bulut, T A Sulaiman, H M Baskonus and A A Sandulyak Optik 135 327 (2017)

    ADS  Article  Google Scholar 

  43. [43]

    E Tala-Tebue, Z I Djoufack, P H Kamdoum-Tamo and A Kenfack-Jiotsa Optik 174 508 (2018).

    ADS  Article  Google Scholar 

  44. [44]

    A Biswas, Q Zhou, S P Moshokoa, H Triki, M Belic and R T Alqahtani Optik 145 14 (2017)

    ADS  Article  Google Scholar 

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Correspondence to Ahmet Bekir.

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Nestor, S., Houwe, A., Rezazadeh, H. et al. Chirped W-shape bright, dark and other solitons solutions of a conformable fractional nonlinear Schrödinger’s equation in nonlinear optics. Indian J Phys (2021). https://doi.org/10.1007/s12648-020-01961-7

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Keywords

  • Solitons
  • Conformable fractional derivative operator
  • Integrability