Abstract
In this paper, we study three different space-time fractional models of the Schrödinger equation. By using the properties of conformable derivative and fractional complex transform, the bright, dark and singular optical solitons for conformable space–time fractional nonlinear \((1+1)\)-dimensional Schrödinger models are determined.
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Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)
Abdullaha, A., Seadawy, A.R., Jun, W.: Mathematical methods and solitary wave solutions of three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma and its applications. Results Phys. 7, 4269–4277 (2017)
Agrawal, G.P.: Nonlinear fiber optics: its history and recent progress [Invited]. J. Opt. Soc. America B 28, A1–A10 (2011)
Arshad, M., Seadawy, Aly R., Lu, Dianchen: Exact bright-dark solitary wave solutions of the higher-order cubic-quintic nonlinear Schrödinger equation and its stability, Optik 128, 40–49 (2017)
Darvishi, M.T., Ahmadian, S., Baloch Arbabi, S., Najafi, M.: Optical solitons for a family of nonlinear (1+1)-dimensional time-space fractional Schrödinger models. Opt. Quantum Electron. 50, 1–20 (2018)
Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S.S.: Exact solutions to the space-time fractional Schrödinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation . Opt. Quantum Electron. 49, 1–13 (2017)
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
Kumar, H., Chand, F: Dark and bright solitary wave solutions Of the higher order nonlinear Schröodinger equation with self-steepening and Self-frequency shift effects. J. Nonlinear Opt Phys. Mater. 22, 1–8 (2013)
Kumar, D., Darvishi, M.T., Joardar, A.K.: Modified Kudryashov method and its application to the fractional version of the variety of Boussinesq-like equations in shallow water. Opt. Quantum Electron. 50, 1–18 (2018)
Kumar, D., Seadawy, A.R., Joardar, A.K.: Modified Kudryashov method via new exact solutions for some conformable fractional differential equations arising in mathematical biology. Chinese Journal of Physics 56, 75–85 (2018)
Kurt, A., Tasbozan, O., Baleanu, D.: New solutions for conformable fractional Nizhnik-Novikov-Veselov system via \((\frac{G^{\prime }}{G})\)-expansion method and homotopy analysis method. Opt. Quantum Electron. 49, 1–10 (2017)
Lu, Dianchen, Seadawy, A.R., Arshad, M.: Bright-dark solitary wave and elliptic function solutions of unstable nonlinear Schr\({\ddot{o}}\)dinger equation and their applications. Opt. Quantum Electron 50, 23 (2018). https://doi.org/10.1007/s11082-017-1294-y
Pawlik, M., Rowlands, G.: The propagation of solitary waves in piezoelectric semiconductors. J. Phys. C 8, 1189–1204 (1975)
Pedlosky, V.E.: Finite-amplitude baroclinic waves. J. Atmos. Sci. 27, 15–30 (1970)
Seadawy, A.R.: Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods. Eur. Phys. J. Plus 132, 518 (2017). https://doi.org/10.1140/epjp/i2017-11755-6
Seadawy, A.R., El-Rashidy, K.: Traveling wave solutions for some coupled nonlinear evolution equations. Mathematical and Computer Modelling 57, 1371–1379 (2013)
Wazwaz, A.M.: A study on linear and nonlinear Schrödinger equations by the variational iteration method. Chaos Solitons Fractals 37, 1136–1142 (2008)
Zhang, W.: Generalized variational principle for long water-wave equation by He’s semi-inverse method. Math. Probl. Eng. 2009, 1–6 (2009)
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Darvishi, M.T., Najafi, M. & Seadawy, A.R. Dispersive bright, dark and singular optical soliton solutions in conformable fractional optical fiber Schrödinger models and its applications. Opt Quant Electron 50, 181 (2018). https://doi.org/10.1007/s11082-018-1448-6
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DOI: https://doi.org/10.1007/s11082-018-1448-6