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Extended classical optical solitons to a nonlinear Schrodinger equation expressing the resonant nonlinear light propagation through isolated flaws in optical waveguides

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Abstract

This study establishes the extended classical optical solitons for a nonlinear Schrodinger equation describing resonant nonlinear light propagation through isolated flaws in optical wave guides. We use the modified Sardar sub-equation approach to get such innovative results. The innovative optical solitons solutions have been investigated to explain unique physical obstacles, and they entail an extended classical M-truncated derivative, which affects the physical properties of the findings greatly. These advancements have been shown to be beneficial in the transmission of long-wave and high-power communications networks. Furthermore, the figures for the acquired solutions are graphed through the depiction of the 3D and contour plots in order to throw additional light on the peculiarities of the obtained solutions.

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References

  • Akinyemi, L., Akpan, U., Veeresha, P., Rezazadeh, H.: M. Inc, Computational techniques to study the dynamicsof generalized unstable nonlinear Schrodinger equation. J. Ocean Eng. Sci. https://doi.org/10.1016/j.joes.2022.02.011 (2022)

  • Ardourel, V., Jebeile, J.: On the presumed superiority of analytical solutions over numerical methods. Eur. J. Philos. Sci. 7(2), 201–20 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Assas, L.M.B.: New exact solutions for the Kawahara equation using Exp-function method. J. Comput. Appl. Math. 233, 97–102 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Babelon, O., Bernard, D., Talon, M.: Introduction to classical integrable systems. Cambridge University Press, Cambridge. 17 Apr 2003

  • Biswas, A.: A pertubation of solitons due to power law nonlinearity, Chaos Solit. Fractals 12, 579–588 (2001)

    Article  Google Scholar 

  • Biswas, A., Suarez, P.: Exact 1-soliton solution of the Zakharov–Kuznetsov equation in plasmas with power law nonlinearity. Appl. Math. Comput. 217(17), 7372–7375 (2011)

    MathSciNet  MATH  Google Scholar 

  • El-Horbati, M.M., Ahmed, F.M.: The solitary travelling wave solutions of some nonlinear partial differential equations using the modified extended tanh function method with Riccati equation. Asian Res. J. Math. 8(3), 1–13 (2018)

    Article  Google Scholar 

  • Eslami, M., Mirzazadeh, M.: Topological 1-soliton of nonlinear Schrödinger equation with dual power nonlinearity in optical fibers. Eur. Phys. J. Plus 128, 141–147 (2013)

    Article  Google Scholar 

  • Goodman, R.H., Holmes, P.J., Weinstein, M.I.: Strong NLS soliton defect interactions. Phys. D 192, 215–248 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Gu, C.: Soliton Theory and its Applications. Springer Science and Business Media, Shanghai (2013)

    Google Scholar 

  • Kayum, M.A., Akbar, M.A., Osman, M.S.: Competent closed form soliton solutions to the nonlinear transmission and the low-pass electrical transmission lines. Eur. Phys. J. Plus 135(7), 1–20 (2020)

    Article  Google Scholar 

  • Kayum, M.A., Ara, S., Barman, H.K., et al.: Soliton solutions to voltage analysis in nonlinear electrical transmission lines and electric signals in telegraph lines. Res. Phys. 18, 103269 (2020)

    Google Scholar 

  • Khan, K., Akbar, M.A.: Travelling wave solutions of the (2 + 1)-dimensional Zoomeron equation and the Burgers equation via the MSE method and the Exp-function method. Ain Shams Eng. J. 5, 247–256 (2014)

    Article  Google Scholar 

  • Kumar, D., Kaplan, M., Haque, M., et al.: A variety of novel exact solutions for different models with conformable derivative in shallow water. Front. Phys. 8, 177 (2020)

    Article  Google Scholar 

  • Nestor, S.: New Jacobi elliptic solutions and other solutions with quadratic-cubic nonlinearity using two mathematical methods. Asian Eur. J. Math. 13, 2050043 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Nestor, S.: Exact traveling wave solutions to the higher-order nonlinear Schrödinger equation having Kerr nonlinearity form using two strategic integrations. Eur. Phys. J. Plus 135, 380 (2020)

    Article  Google Scholar 

  • Nestor, S., 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. 96, 243–255 (2022)

    Article  ADS  Google Scholar 

  • Pandir, Y., Yildirim, A.: Analytical approach for the fractional differential equation by using the extended tanh method. Waves Random. Compl. Media. 28(3), 1745–5049 (2017)

    MathSciNet  Google Scholar 

  • Rezazadeh, H., et al.: Computational solutions of the generalized Ito equation in nonlinear dispersive systems. Int. J. Mod. Phys. B 35(13), 2150172 (2021)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Segata, J.-I.: Final State Problem for the Cubic Nonlinear Schr\({\ddot{\bf o}}\)dinger Equation with Repulsive Delta Potential. Commun. Partial Diff. Eqn. 40(2), 309–328 (2015)

    Article  MATH  Google Scholar 

  • Sousa, J.V.D.C., de Oliveira, E.C.: A new truncated M-fractional derivative type unifying some fractional derivative types with classical properties. Int. J. Anal. Appl. 16(1), 83–96 (2018)

    MATH  Google Scholar 

  • Tao, G., et al.: Dynamics of a new class of solitary wave structures in telecommunications systems via a (2+1)-dimensional nonlinear transmission line. Mod. Phys. Lett.B 36(19), 2150596 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  • Triki, H., Biswas, A.: Dark solitons for a generalized nonlinear Schrödinger equation with parabolic law and dual power nonlinearity. Math. Methods Appl. Sci. 34, 958–962 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Wang, M., Tian, B., Sun, Y., et al.: Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3 + 1)-dimensional nonlinear wave equation for a liquid with gas bubbles. Comput. Math. Appl. 79(3), 576–587 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  • Wazwaz, A.M.: A sine-cosine method for handling nonlinear wave equations. Math. Comput. Model. 40, 499–508 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Yamgoue, S.B., Deffo, G.R., Pelap, F.B.: A new rational sine-Gordon expansion method and its application to nonlinear wave equations arising in mathematical physics. Eur. Phys. J. Plus. 134, 380 (2019)

    Article  Google Scholar 

  • Yin, H.M., Tian, B., Zhao, X.C.: Chaotic breathers and breather fission/fusion for a vector nonlinear Schrödinger equation in a birefringent optical fiber or wavelength division multiplexed system. Appl. Math. Comput. 368, 124768 (2020)

    MathSciNet  MATH  Google Scholar 

  • Zerrad, E., Biswas, A., Kohl, R., Milovic, D.: Optical solitons by He’s variational principle in a non-kerr law media. J. Infrared Millim. Terahertz Waves 30(5), 526–537 (2009)

    Article  Google Scholar 

  • Zhang, C.R., Tian, B., Qu, Q.X., et al.: Vector bright solitons and their interactions of the couple FokasLenells system in a birefringent optical fiber. Zeitsch Angew Math. Phys. 71(1), 1–19 (2020)

    ADS  Google Scholar 

  • Zhao, D., Zhaqilao: Three-wave interactions in a more general (2+1)-dimensional Boussinesq equation, Eur. Phys. J. Plus, 135, 617 (2020)

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Authors and Affiliations

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

    Abdullahi Yusuf & Tukur A. Sulaiman

  2. Department of Mathematics, King Abdul Aziz University, Jeddah, Saudi Arabia

    Ali S. Alshomrani

  3. Department of Statistics School of Technology, Kano State Polytechnic, Kano, Nigeria

    Ibrahim Isah

  4. Department of Mathematics, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  5. Institute of Space Sciences, Magurele,Bucharest, Romania

    Dumitru Baleanu

  6. Lebanese American University, Beirut, 11022801, Lebanon

    Dumitru Baleanu

Authors
  1. Abdullahi Yusuf
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  2. Ali S. Alshomrani
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  3. Tukur A. Sulaiman
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  4. Ibrahim Isah
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  5. Dumitru Baleanu
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Contributions

AY: Formal analysis, Writing—original draft, Writing—review and editing. ASA: Supervision, review and editing. TAS: Conceptualization, Formal analysis, Writing—original draft, Writing—review and editing. II: Formal analysis, Writing—review and editing. DB: Supervision, review and editing.

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Correspondence to Tukur A. Sulaiman.

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Yusuf, A., Alshomrani, A.S., Sulaiman, T.A. et al. Extended classical optical solitons to a nonlinear Schrodinger equation expressing the resonant nonlinear light propagation through isolated flaws in optical waveguides. Opt Quant Electron 54, 853 (2022). https://doi.org/10.1007/s11082-022-04268-5

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