Abstract
A nonlinear Schrödinger equation describing the polarization mode in an optical fiber which involves different physical terms such as quintic nonlinearity, self-steepening effect, and self-frequency shift is investigated in the present paper. The study goes on by adopting a field function and effective ansatzes to arrive at a highly nonlinear ODE which is formally solved with the help of the modified Kudryashov and \(exp_{a}\)-function methods. As a result, a series of chirped optical solitons along with nonlinear chirps is retrieved, confirming the fantastic performance of schemes.
Similar content being viewed by others
References
Ali, A.T., Hassan, E.R.: General function method for nonlinear evolution equations. Appl. Math. Comput. 217, 451–459 (2010)
Alka, A., Goyal, R., Gupta, C.N.K.: Chirped femtosecond solitons and double-kink solitons in the cubic-quintic nonlinear Schrödinger equation with self-steepening and self-frequency shift. Phys Rev A 84, 063830 (2011)
Biswas, A., Ekici, M., Sonmezoglu, A., Alqahtani, R.T.: Optical soliton perturbation with full nonlinearity for Fokas-Lenells equation. Optik 165, 29–34 (2018c)
Biswas, A., Yildirim, Y., Yasar, E., Alqahtani, R.T.: Optical solitons for Lakshmanan–Porsezian–Daniel model with dual-dispersion by trial equation method. Optik 168, 432–439 (2018b)
Biswas, A., Yildirim, Y., Yasar, E., Triki, H., Alshomrani, A.S., Ullah, M.Z., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical soliton perturbation with full nonlinearity for Gerdjikov–Ivanov equation by trial equation method. Optik 157, 1214–1218 (2018a)
Desaix, M., Helczynski, L., Anderson, D., Lisak, M.: Propagation properties of chirped soliton pulses in optical nonlinear Kerr media. Phys. Rev. E 65, 056602 (2002)
Fan, X., Qu, T., Huang, S., Chen, X., Cao, M., Zhou, Q., Liu, W.: Analytic study on the influences of higher-order effects on optical solitons in fiber laser. Optik 186, 326–331 (2019)
He, J.H., Wu, X.H.: Exp-function method for nonlinear wave equations. Chaos Solitons Fract. 30, 700–708 (2006)
Hosseini, K., Ansari, R., Samadani, F., Zabihi, A., Shafaroody, A., Mirzazadeh, M.: High-order dispersive cubic-quintic Schrödinger equation and its exact solutions. Acta Phys. Pol., A 136, 203–207 (2019b)
Hosseini, K., Kaur, L., Mirzazadeh, M., Baskonus, H.M.: 1-soliton solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative. Opt. Quant. Electron. 53, 125 (2021)
Hosseini, K., Mirzazadeh, M., Ilie, M., Gómez-Aguilar, J.F.: Soliton solutions of the Sasa-Satsuma equation in the monomode optical fibers including the beta-derivatives. Optik 224, 165425 (2020b)
Hosseini, K., Mirzazadeh, M., Rabiei, F., Baskonus, H.M., Yel, G.: Dark optical solitons to the Biswas-Arshed equation with high order dispersions and absence of self-phase modulation. Optik 209, 164576 (2020c)
Hosseini, K., Mirzazadeh, M., Vahidi, J., Asghari, R.: Optical wave structures to the Fokas-Lenells equation. Optik 207, 164450 (2020d)
Hosseini, K., Mirzazadeh, M., Zhou, Q., Liu, Y., Moradi, M.: Analytic study on chirped optical solitons in nonlinear metamaterials with higher order effects. Laser Phys. 29, 095402 (2019a)
Hosseini, K., Osman, M.S., Mirzazadeh, M., Rabiei, F.: Investigation of different wave structures to the generalized third-order nonlinear Scrödinger equation. Optik 206, 164259 (2020a)
Hosseini, K., Yazdani Bejarbaneh, E., Bekir, A., Kaplan, M.: New exact solutions of some nonlinear evolution equations of pseudoparabolic type. Opt. Quant. Electron. 49, 241 (2017)
Hosseini, K., Zabihi, A., Samadani, F., Ansari, R.: New explicit exact solutions of the unstable nonlinear Schrӧdinger’s equation using the expa and hyperbolic function methods. Opt. Quant. Electron. 50, 82 (2018)
Ilie, M., Biazar, J., Ayati, Z.: Analytical study of exact traveling wave solutions for time-fractional nonlinear Schrödinger equations. Opt. Quant. Electron. 50, 413 (2018a)
Ilie, M., Biazar, J., Ayati, Z.: Resonant solitons to the nonlinear Schrödinger equation with different forms of nonlinearities. Optik 164, 201–209 (2018b)
Korkmaz, A., Hosseini, K.: Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods. Opt. Quant. Electron. 49, 278 (2017)
Kruglov, V.I., Peacock, A.C., Harvey, J.D.: Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients. Phys. Rev. Lett. 90, 113902 (2003)
Kudryashov, N.A.: One method for finding exact solutions of nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulations 17, 2248–2253 (2012)
Liu, W., Pang, L., Han, H., Bi, K., Lei, M., Wei, Z.: Tungsten disulphide for ultrashort pulse generation in all-fiber lasers. Nanoscale 9, 5806–5811 (2017b)
Liu, W., Pang, L., Han, H., Liu, M., Lei, M., Fang, S., Teng, H., Wei, Z.: Tungsten disulfide saturable absorbers for 67 fs mode-locked erbium-doped fiber lasers. Opt. Express 25, 2950 (2017a)
Liu, W., Pang, L., Han, H., Shen, Z., Lei, M., Teng, H., Wei, Z.: Dark solitons in WS2 erbium-doped fiber lasers. Photon. Res. 4, 111–114 (2016)
Liu, X., Triki, H., Zhou, Q., Liu, W., Biswas, A.: Analytic study on interactions between periodic solitons with controllable parameters. Nonlinear Dyn. 94, 703–709 (2018b)
Liu, W., Zhu, Y.N., Liu, M., Wen, B., Fang, S., Teng, H., Lei, M., Liu, L.M., Wei, Z.: Optical properties and applications for MoS2-Sb2Te3-MoS2 heterostructure materials. Photon. Res. 6, 220 (2018a)
Tala-Tebue, E., Djoufack, Z.I., Yamgoue, S.B., Kenfack-Jiotsa, A., Kofané, T.C.: Chirped soliton solutions in optical medium. Opt. Quant. Electron. 51, 7 (2019)
Triki, H., Bensalem, C., Biswas, A., Zhou, Q., Ekici, M., Moshokoa, S.P., Belic, M.: shaped and bright optical solitons in negative indexed materials. Chaos Solitons Fract. 123, 101–107 (2019)
Triki, H., Biswas, A., Babatin, M.M., Zhou, Q.: Chirped dark solitons in optical metamaterials. Optik 158, 312–315 (2018a)
Triki, H., Biswas, A., Milovic, D., Belic, M.: Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities. Opt. Commun. 366, 362–369 (2016b)
Triki, H., Porsezian, K., Grelu, P.: Chirped soliton solutions for the generalized nonlinear Schrödinger equation with polynomial nonlinearity and non-Kerr terms of arbitrary order. J. Opt. 18, 075504 (2016a)
Triki, H., Zhou, Q., Moshokoa, S.P., Ullah, M.Z., Biswas, A., Belic, M.: Novel singular solitons in optical metamaterials for self-steepening effect. Optik 154, 545–550 (2018b)
Vyas, V.M., Patel, P., Panigrahi, P.K., Kumar, C.N., Greiner, W.: Chirped chiral solitons in the nonlinear Schrödinger equation with self-steepening and self-frequency shift. Phys. Rev. A 78, 021803(R) (2008)
Wang, C., Nie, Z., Xie, W., Gao, J., Zhou, Q., Liu, W.: Dark soliton control based on dispersion and nonlinearity for third-order nonlinear Schrödinger equation. Optik 184, 370–376 (2019)
Yan, Y., Liu, W., Zhou, Q., Biswas, A.: Dromion-like structures and periodic wave solutions for variable-coefficients complex cubic-quintic Ginzburg-Landau equation influenced by higher-order effects and nonlinear gain. Nolinear Dyn. 99, 1313–1319 (2020)
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Eslami, M., Hosseini, K., Matinfar, M. et al. A nonlinear Schrödinger equation describing the polarization mode and its chirped optical solitons. Opt Quant Electron 53, 314 (2021). https://doi.org/10.1007/s11082-021-02917-9
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-021-02917-9