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A variety of structures of optical solitons for the nonlinear Schrödinger equation with generalized anti-cubic nonlinearity

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Abstract

Nonlinear Schrödinger equation plays a significant role in the description of propagation of light in nonlinear optical fibers. In this manuscript, the nonlinear Schrödinger equation is considered with anti-cubic law of nonlinearity. Chirped optical soliton solutions and chirp-free solutions are extracted for the proposed equation using the generalized projective Riccati equation technique and two variables \(\left( \frac{G'}{G},\frac{1}{G}\right)\)-expansion technique. To better comprehend the dynamic characteristics of the retrieved solutions their graphical visualization are provided.

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The computations involved in the work are done with the help of Maple and Mathematica.

References

  • Akram, G., Sadaf, M., Arshed, S., Sameen, F.: Bright, dark, kink, singular and periodic soliton solutions of Lakshmanan–Porsezian–Daniel model by generalized projective Riccati equations method. Optik 241, 167051 (2021)

    Article  ADS  Google Scholar 

  • Al-Ghafri, S.K., Krishnan, V.E., Biswas, A.: Chirped optical soliton perturbation of Fokas–Lenells equation with full nonlinearity. Adv. Differ. Equ. 2020, 191 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  • Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.: Chirped and Chirp-free optical solitons with anti-cubic nonlinearity by extended trial function method. Optik 178, 636–644 (2019)

    Article  ADS  Google Scholar 

  • Dutta, H., Günerhan, H., Ali, K., Yilmazer, R.: Exact soliton solutions to the cubic-quartic non-linear Schrödinger equation with conformable derivative. Front. Phys. 8, 62 (2020). https://doi.org/10.3389/fphy.2020.00062

    Article  Google Scholar 

  • Gao, W., Ismael, F.H., Husien, M.A., Bulut, H., Baskonus, M.H.: Optical soliton solutions of the Cubic-Quartic nonlinear Schrödinger and resonant nonlinear Schrödinger equation with the Parabolic Law. Appl. Sci. 10(1), 219 (2019)

    Article  Google Scholar 

  • Houwe, A., Justin, M., Jerome, D., Betchewe, G., Doka, S.Y., Crepin, T.K.: Solitons solutions of nonlinear Schrödinger equation in the left-handed metamaterials by three different techniques. J. Phys. Commun. 3, 011002 (2019)

    Article  Google Scholar 

  • Mai, L.X., Li, W., Dong, H.S.: Exact solutions to the nonlinear Schrödinger equation with time dependent coefficients. Adv. High Energy Phys. 2021, 6694980 (2021)

    Article  Google Scholar 

  • Miah, M.M., Ali, S.M.H., Akbar, A.M., Seadawy, R.A.: New applications of the two variable \(\left(\frac{G^{\prime }}{G},\frac{1}{G}\right)\)-expansion method for closed form traveling wave solutions of integro-differential equation. J. Ocean Eng. Sci. 4(2), 132–143 (2019)

    Article  Google Scholar 

  • Nowehy, A., Ghani, A.: The Riccati equation method combined with the generalized extended \(\left(\frac{G^{\prime }}{G}\right)\)-expansion method for solving the nonlinear kpp equation. J. Math. Res. Appl. 37, 577–590 (2017)

    MathSciNet  Google Scholar 

  • Rezazadeh, H., Adel, W., Eslami, M., Tariq, U.K., Alizamini, M.S., Bekir, A., Chu, M.Y.: On the optical solutions to nonlinear Schrödinger equation with second-order spatiotemporal dispersion. Open Phys. 19, 111–118 (2021)

    Article  Google Scholar 

  • Samir, I., Badra, N., Seadawy, A.R., Ahmed, H.M., Arnous, A.H.: Exact wave solutions of the fourth order non-linear partial differential equation of optical fiber pulses by using different methods. Optik 230, 166313 (2021)

    Article  ADS  Google Scholar 

  • Samir, I., Badra, N., Ahmed, H.M., Arnous, A.H.: Optical soliton perturbation with Kudryashov’s generalized law of refractive index and generalized nonlocal laws by improved modified extended tanh method. Alex. Eng. J. 61(5), 3365–3374 (2022)

    Article  Google Scholar 

  • Samir, I., Badra, N., Ahmed, H.M., Arnous, A.H.: Optical solitons and other solutions for coupled system of nonlinear Schrödinger’s equation with parabolic nonlocal law of refractive index by using the improved modified extended tanh function method. Optik 254, 168602 (2022)

    Article  ADS  Google Scholar 

  • Samir, I., Badra, N., Ahmed, H.M., Arnous, A.H.: Exploring soliton solutions to sixth order dispersive non-linear Schrödinger equation with Kerr law nonlinearity using modified extended direct algebraic method. Opt. Quant. Electron. 55(2), 184 (2023)

    Article  Google Scholar 

  • Shahoot, M.A., Alurrfi, E.A.K., Elmrid, M.M., Almsiri, M.A., Arwiniya, H.M.A.: \(\left(\frac{G^{\prime }}{G},\frac{1}{G}\right)\)-expansion method for solving a nonlinear PDE describing the nonlinear low-pass electrical lines. J. Taibah Univ. Sci. 13, 63–70 (2018)

    Article  Google Scholar 

  • Sirisubtawee, S., Koonprasert, S., Sungnul, S.: Some Applications of the \(\left(\frac{G^{\prime }}{G},\frac{1}{G}\right)\)-expansion method for finding exact traveling wave solution of nonlinear fractional evolution equation. Symmetry 11(8), 952 (2019)

    Article  ADS  Google Scholar 

  • Zafar, A., Raheel, M., Rezazadeh, H., Inc, M., Akinlar, A.M.: New Chirp-free and Chirped form Optical solitons to the nonlinear Schrödinger equation. Opt. Quant. Electron. 53, 604 (2021)

    Article  Google Scholar 

  • Zayed, E.M.E., Alurrfi, E.A.K.: The \(\left(\frac{G^{\prime }}{G},\frac{1}{G}\right)\)-expansion method and its applications for solving two higher order nonlinear evolution equations. Math. Probl. Eng. 2014, 746538 (2014)

    Article  MATH  Google Scholar 

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Correspondence to Saima Arshed.

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Arshed, S., Akram, G., Sadaf, M. et al. A variety of structures of optical solitons for the nonlinear Schrödinger equation with generalized anti-cubic nonlinearity. Opt Quant Electron 55, 542 (2023). https://doi.org/10.1007/s11082-023-04792-y

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