Abstract
The main target of this work is implementing multiple accurate cubic optical solitons for the nonlinear Schrödinger equation in the presence of third-order dispersion effects, absence of the chromatic dispersion. The emergence cubic optical solitons of the proposed model are extracted for the Kerr-Law and Power-Law nonlinearity in the framework of two distinct techniques, the first one is the extended simple equation method (ESEM), while the other is the solitary wave ansatz method (SWAM). These cubic optical solitons for the Kerr-Law and Power- Law nonlinearity have been extracted successfully at the same time and parallel via these two different techniques. A good comparison not only between our achieved results by these two manners but also with that achieved previously has been extracted.
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Bansal, A., Biswas, A., Zhou, Q., Babatin, M.M.: Lie symmetry analysis for cubic-quartic nonlinear Schrödinger’s equation. Optik 169, 12–15 (2018)
Bekir, A., Zahran, E.H.M.: Painleve approach and its applications to get new exact solutions of three biological models instead of its numerical solutions. Int. J. Mod. Phys. B 34, 2050270 (2020)
Bekir, A., Zahran, E.H.M.: Optical soliton solutions of the thin-film ferro-electric materials equation according to the Painlevé approach. Opt. Quantum Electron. 53, 118 (2021)
Bekir, A., Zahran, E.H.M.: New vision for the soliton solutions to the complex Hirota-dynamical model. Physica Scripta 96, 055212 (2021)
Bekir, A., Zahran, E.H.M.: Bright and dark soliton solutions for the complex Kundu-Eckhaus equation. Optik-Int. J. Light Electron Opt. 223, 165233 (2020)
Bekir, A., Zahran, E.H.M.: Three distinct and impressive visions for the soliton solutions to the higher-order nonlinear Schrödinger equation. Opt.—Int. J. Light Electron Opt. 228, 166157 (2021)
Bekir, A., Zahran, E.H.M.: New visions of the soliton solutions to the modified nonlinear Schrödinger equation; Optik 232, 166539 (2021)
Bekir, A., Shehata, M.S.M., Zahran, E.H.M: Comparison between the new exact and numerical solutions of the Mikhailov-Novikov-Wang equation, Numerical Method of Partial Differential Equation journal (in press)
Biswas, A.: 1-Soliton solution of the K(m; n) equation with generalized evolution. Phys. Lett. A 372, 4601–4602 (2008)
Biswas, A., Arshed, S.: Application of semi-inverse variational principle to cubic-quartic optical solitons with Kerr and power law nonlinearity. Optik 172, 847–850 (2018)
Biswas, A., Triki, H., Zhou, Q., Moshokoa, S.P., Ullah, M.Z., Belic, M.: Cubic-quartic optical solitons in Kerr and power law media. Optik 144, 357–362 (2017a)
Biswas, A., Kara, A.H., Ullah, M.Z., Zhou, Q., Triki, H., Belic, M.: Conservation laws for cubic-quartic optical solitons in Kerr and power law media. Optik 145, 650–654 (2017b)
Blanco-Redondo, A., Sterke, C.M.d., Sipe, J.E., Krauss, T.F., Eggleton, B.J., Husko, C.: Pure-quartic solitons. Nat. Commun. 7, 10427 (2016)
Das, A., Biswas, A., Ekici, M., Khan, S., Zhou, Q., Moshokoa, S.P.: Suppressing internet bottleneck with fractional temporal evolution of cubic-quartic optical solitons. Optik 182, 303–307 (2019)
El-Ganaini, S.I.A.: The first integral method to the nonlinear Schrödinger equations in higher dimensions. Abst. Appl. Anal. 10, 349173 (2013)
Gonzalez-Gaxiola, O., Biswas, A., Mallawi, F., Belic, M.: Cubic-quartic bright optical solitons by improved Adomian decomposition method. J. Adv. Res. 21, 161–167 (2020)
Hosseini, K., Osman, M.S., Mirzazadeh, M., Rabiei, F.: Investigation of different wave structures to the generalized third-order nonlinear Schrödinger equation. Optik 206, 164259 (2020)
Huang, D.J., Li, D.S., Zhang, H.Q.: Explicit and exact travelling wave solutions for the generalized derivative Schrödinger equation. Chaos Solitons Fract. 31, 586–593 (2007)
Kodama, Y., Hasegawa, A.: Solitons in Optical Communications. Oxford University Press, Oxford (1995)
Kohl, R.W., Biswas, A., Ekici, M., Zhou, Q., Moshokoa, S.P., Belic, M.R.: Cubic-quartic optical soliton perturbation by semi-inverse variational principle. Optik 185, 45–49 (2019)
Kudryashov, N.A.: Solitary wave solutions of hierarchy with non-local nonlinearity. Appl. Math. Lett. 103, 106155 (2020)
Kudryashov, N.A.: Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations. Appl. Math. Comput. 371, 124972 (2020)
Kudryashov, N.A.: Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation. Optik 206, 164335 (2020)
Kudryashov, N.A.: Mathematical model of propagation pulse in optical fiber with power nonlinearities. Optik 212, 164750 (2020)
Liu, C.: Exact solutions for the higher-order nonlinear Schrödinger equation in nonlinear optical fibres. Chaos Solitons Fract. 23, 949–955 (2005)
Li, B., Zhao, J., Pan, A., Mirzazadeh, M., Ekici, M., Zhou, Q., Liu, W.: Stable propagation of optical solitons in fiber lasers by using symbolic computation. Optik 178, 142–145 (2019)
Mirzazadeh, M., Eslami, M., Biswas, A.: Dispersive optical solitons by Kudryashov’s method. Optik 125(23), 6874–6880 (2014)
Shehata, M.S.M., Rezazadeh, H., Jawad, A.J.M., Zahran, E.H.M., Bekir, A.: Optical solitons to a perturbed Gerdjikov-Ivanov equation using two different techniques. Revista Mexicana de Fisica 67, 050704 (2021)
Triki, H., Wazwaz, A.M.: Bright and dark soliton solutions for a K(m; n) equation with t-dependent coefficients. Phys. Lett. A 373, 2162–2165 (2009)
Triki, H., Wazwaz, A.M.: Bright and dark solitons for a generalized Korteweg–de Vries-modified Korteweg–de Vries equation with high-order nonlinear terms and time-dependent coefficients. Can. J. Phys. 89, 253–259 (2011)
Wazwaz, A.M., Xu, G.Q.: Bright, dark, and Gaussons optical solutions for fourth order Schrödinger equation with cubic-quantic and logarithmic nonlinearities. Optik 202, 163564 (2020)
Xiao, L.L., Liang, W.M.: The (G′/G)-Expansion Method and travelling wave solutions for a higher-order nonlinear Schrödinger equation. Appl. Math. Comput. 208, 440–445 (2009)
Yildirim, Y., Biswas, A., Jawad, A.J.M., Ekici, M., Zhou, Q., Khan, S., Alzahrani, A.K., Belic, M.R.: Cubic-quartic optical solitons in birefringent fibers with four forms of nonlinear refractive index by exp-function expansion. Results Phys.16, 102913 (2020)
Yildirim, Y., Biswas, A., Guggilla, P., Mallawi, F., Belic, M.R.: Cubic-quartic optical solitons in birefringent fibers with four forms of nonlinear refractive index. Optik 203, 163885 (2020)
Yıldırım, Y., Biswas, A., Asma, M., Guggilla, P., Khan, S., Ekici, M., Alzahrani, A.K., Belic, M.R.: Pure-cubic optical soliton perturbation with full nonlinearity. Opt.—Int. J. Light Electron Opt. 222, 165394 (2020)
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Zahran, E.H.M., Bekir, A. Multiple accurate-cubic optical solitons to the kerr-law and power-law nonlinear Schrödinger equation without the chromatic dispersion. Opt Quant Electron 54, 14 (2022). https://doi.org/10.1007/s11082-021-03389-7
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DOI: https://doi.org/10.1007/s11082-021-03389-7