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Optical solitons solutions for perturbed time fractional nonlinear Schrodinger equation via two strategic algorithms

  • Received: 14 November 2019 Accepted: 31 January 2020 Published: 24 February 2020
  • MSC : 35A20, 35A99, 83C15, 65Z05

  • In this work, two algorithms namely, the generalized exp(-w(ξ)) and rational (G'/G2)-expansion methods are suggested for constructing new optical solitons solutions for the perturbed fractional nonlinear Schrodinger equation. The solutions include hyperbolic, trigonometric or rational function. Our results indicate that, group of new solutions are obtained with much reliability, accuracy and efficiency of the proposed methods. Eventually, our pending may become of wide relevance in addition to realize the main features and even propagation of the nonlinear waves in fractal medium.

    Citation: S. Owyed, M. A. Abdou, A. Abdel-Aty, H. Dutta. Optical solitons solutions for perturbed time fractional nonlinear Schrodinger equation via two strategic algorithms[J]. AIMS Mathematics, 2020, 5(3): 2057-2070. doi: 10.3934/math.2020136

    Related Papers:

  • In this work, two algorithms namely, the generalized exp(-w(ξ)) and rational (G'/G2)-expansion methods are suggested for constructing new optical solitons solutions for the perturbed fractional nonlinear Schrodinger equation. The solutions include hyperbolic, trigonometric or rational function. Our results indicate that, group of new solutions are obtained with much reliability, accuracy and efficiency of the proposed methods. Eventually, our pending may become of wide relevance in addition to realize the main features and even propagation of the nonlinear waves in fractal medium.


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    [1] G. A. Zakeri, E. Yomba, Exact solutions of a generalized autonomous Duffing-type equation Appl. Math. Model., 39 (2015), 4607-4616.
    [2] A. Biswas, D. Milovic, Bright and dark solitons of the generalized nonlinear Schrödinger's equation, Commun. Nonlinear Sci. Numer. Simul., 15 (2010), 1473-1484. doi: 10.1016/j.cnsns.2009.06.017
    [3] A. Atangana, K. M. Owolabi, New numerical approach for fractional differential equations, Math. Model. Nat. Phenom., 13 (2018), 3-24. doi: 10.1051/mmnp/2018010
    [4] M. S. Abdalla, S. S. Hassan, M. Abdel-Aty, Entropic uncertainty in the Jaynes Cummings model in presence of a second harmonic generation, Optics Commun., 244 (2005), 431-443. doi: 10.1016/j.optcom.2004.09.051
    [5] A. M. Wazwaz, Multiple complex soliton solutions for the integrable Sinh-Gordon and the modified KdV-Sinh-Gordon equation, Appl. Math. Inf. Sci., 12 (2018), 899-905. doi: 10.18576/amis/120501
    [6] A. Atangana, A. Secer, The time-fractional coupled-Korteweg-de-Vries equations, Abstr. Appl. Anal., (2013), Article ID 947986, 8 pages.
    [7] O. Ozturk, R. Yilmazer, On applications of the fractional calculus for some singular differential equations, Prog. Frac. Diff. Appl., 4 (2018), 27-33. doi: 10.18576/pfda/040104
    [8] D. Kumar, J. Singh, A. Prakash, et al., Numerical simulation for system of time-fractional linear and nonlinear differential equations, Progr. Fract. Differ. Appl., 5 (2019), 65-77. doi: 10.18576/pfda/050107
    [9] A. H. M. Ahmed, L. Y. Cheong, N Zakaria, et al., Statistical properties of a Raman three-level atom interacting with a cavity field, AIP Conf. Proc., 1482 (2012), 373-375.
    [10] A. H. M. Ahmed, L. Y. Cheong, N. Zakaria, et al., Dynamics of information coded in a single cooper pair box, Int. J. Theor. Phys., 52 (2012), 1979-1988.
    [11] E. Yaşar, Y. Yıldırım, E. Yaşar, New optical solitons of space-time conformable fractional perturbed Gerdjikov-Ivanov equation by sine-Gordon equation method, Results Phys., 9 (2018), 1666-1672. doi: 10.1016/j.rinp.2018.04.058
    [12] A. Cernea, Continuous family of solutions for fractional integro-differential inclusions of Caputo-Katugampola type, Prog. Frac. Diff. Appl., 5 (2019), 37-42. doi: 10.18576/pfda/050104
    [13] A. Sardar, S. M. Husnain, S. Rizvi, et al., Multiple travelling wave solutions for electrical transmission line model, Nonlinear Dyn., 82 (2015), 1317-1324. doi: 10.1007/s11071-015-2240-9
    [14] Y. Liu, Existence of solutions of multi-point boundary value problems for fractional differential systems with impulse effects, Prog. Frac. Diff. Appl., 3 (2017), 111-140. doi: 10.18576/pfda/030204
    [15] M. Younis, S. Ali, S. A. Mahmood, Solitons for compound KdV-Burgers equation with variable coefficients and power law nonlinearity, Nonlinear Dyn., 81 (2015), 1191-1196. doi: 10.1007/s11071-015-2060-y
    [16] M. Younis, S. T. R. Rizvi, Optical solitons for ultrashort pulses in nano fibers, J. Nanoelectron. Optoelectron., 10 (2015) 179-182.
    [17] Q. Zhou, D. Yao, F. Chen, et al., Optical solitons in gas-filled, hollow-core photonic crystal fibers with inter-modal dispersion and self-steepening, J. Mod. Opt., 60 (2013), 854-859. doi: 10.1080/09500340.2013.816384
    [18] A. Biswas, 1-soliton solution of ()-dimensional nonlinear Schrödinger's equation in dual-power law media, Phys. Lett. A., 372 (2008), 5941-5943. doi: 10.1016/j.physleta.2008.07.052
    [19] A. Biswas, Y. Yildirm, E. Yasar, et al., Optical soliton solutions to Fokas-lenells equation using some different methods, Optik, 173 (2018), 21-31. doi: 10.1016/j.ijleo.2018.07.098
    [20] A. Atangana, D. Baleanu, New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model, Thermal Sci., 20 (2016), 763-769. doi: 10.2298/TSCI160111018A
    [21] A. Biswas, M. Mirzazadeh, M. Eslami, Dispersive dark optical soliton with Schödinger-Hirota equation by G'/G-expansion approach in power law medium, Optik, 125 (2014), 4215-4218. doi: 10.1016/j.ijleo.2014.03.039
    [22] A. Atangana, D. Baleanu, A. Alsaedi, New properties of conformable derivative, Open Math., 13 (2015), 889-898.
    [23] N. Boumaza, T. Benouaz, A. Chikhaoui, et al., Numerical simulation of nonlinear pulses propagation in a nonlinear optical directional coupler, Int. J. Phys. Sci., 4 (2009), 505-513.
    [24] M. G. Hafez, M. A. Akbar, New exact traveling wave solutions to the (1+1)-dimensional Klein-Gordon-Zakharov equation for wave propagation in plasma using the exp(-Φ(ξ))-expansion method, Propul. Power Res., 4 (2015), 31-39. doi: 10.1016/j.jppr.2015.02.002
    [25] M. A. Abdou, S. Owyed, A. Abdel-Aty, et al., Optical soliton solutions for a space-time fractional perturbed nonlinear Schrödinger equation arising in quantum physics, Results Phys., 16 (2020), 102895.
    [26] M. A. Abdou, An analytical method for space-time fractional nonlinear differential equations arising in plasma physics, J. Ocean Eng. Sci., 2 (2017), 288-292. doi: 10.1016/j.joes.2017.09.002
    [27] A. Elhanbaly, M. A. Abdou, On the solution of fractional space-time nonlinear differential equations, Int. J. Appl. Math. Comput., 5 (2013), 47-58.
    [28] Z. Hammouch, M. Toufik, Traveling-wave solutions of the generalized Zakharov equation with time-space fractional derivatives, J. MESA., 4 (2014), 489-498.
    [29] A. R. Hadhoud, Quintic non-polynomial spline method for solving the time fractional biharmonic equation, Appl. Math. Inf. Sci., 13 (2019), 507-513. doi: 10.18576/amis/130323
    [30] L. Qian, R. A. M. Attia, Y. Qiu, et al., On Breather and Cuspon waves solutions for the generalized higher-order nonlinear Schrodinger equation with light-wave promulgation in an optical fiber, Num. Comp. Meth. Sci. Eng., 1 (2019), 101-110.
    [31] A. M. Wazwaz, Study on a new (3+1)-dimensional extensions of the Konopelchenko-Dubrovsky equation, Appl. Math. Inf. Sci., 12 (2018), 1067-1071. doi: 10.18576/amis/120601
    [32] M. A. Abdou, A. A. Soliman, New exact travelling wave solutions for space-time fractional nonlinear equations describing nonlinear transmission lines, Results Phys., 9 (2018), 1497-1501. doi: 10.1016/j.rinp.2018.04.031
    [33] G. Jumarie, Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results, Comput. ‎Math. Appl., 51 (2006), 1367-1376.
    [34] Kh. A. Gepreel, T. A. Nofal, N. S. Al-Sayali, Optical soliton solutions for nonlinear evolution equations in mathematical physics by using the extended (G'/G) expansion function method, J. Compt. Theor. Nanosci., 14 (2017), 979-990. doi: 10.1166/jctn.2017.6391
    [35] N. Alam, F. B. M. Belgacem, Microtubules nonlinear models dynamics investigations through the exp(-Φ(ξ))-expansion method implementation, Mathematics, 4 (2016), 1-13.
    [36] A. S. J. Al-Saif, M. S. Abdul-Wahab, Application of new simulation scheme for the nonlinear biological population model, Num. Comp. Meth. Sci. Eng., 1 (2019), 89-101.
    [37] H. O. Roshid, Md. A. Rahman, The exp(-Φ(η))-expansion method with application in the (1+1)-dimensional classical Boussinesq equations, Results Phys., 4 (2014), 150-155. doi: 10.1016/j.rinp.2014.07.006
    [38] E. M. Zayed, A. G. Al Nowehy, Exact solutions of the Biswas-Milovic equation, the ZK(m,n,k) equation and the K(m,n) equation using the generalized Kudryashov method, Open Phys., 14 (2016), 129-139.
    [39] S. Bibi, S. T. Mohyud-Din, R. Ullah, et al., Exact solutions for STO and (3+1)-dimensional KdV-ZK equations using-expansion method, Results Phys., 7 (2017), 4434-4439. doi: 10.1016/j.rinp.2017.11.009
    [40] M. A. Abdelkawy, I. G. Ameen, A spectral collocation method for coupled system of two dimensional Abel integral equations of the eecond kind, Inf. Sci. Lett., 8 (2019), 89-93.
    [41] Kh. A. Gepreel, Exact solutions for nonlinear integral member of Kadomtsev-Petviashvili hierarchy differential equations using the modified (w/g)- expansion method, Comput. Math. Appl., 72 (2016), 2072-2083. doi: 10.1016/j.camwa.2016.08.005
    [42] H. M. Baskonus, Complex soliton solutions to the Gilson-Pickering model, Axioms, 8 (2019), 18.
    [43] G. Yel, H. M. Baskonus, H. Bulut, Regarding some novel exponential travelling wave solutions to the Wu-Zhang system arising in nonlinear water wave model, Indian J. Phys., 93 (2019), 1031-1039. doi: 10.1007/s12648-018-1347-5
    [44] T. Salahuddin, M. Y. Malik, A. Hussain, et al., Combined effects of variable thermal conductivity and MHD flow on pseudoplastic fluid over a stretching cylinder by using Keller box method, Inf. Sci. Lett., 5 (2016), 11-19. doi: 10.18576/isl/050102
    [45] W. Gao, H. F. Ismael, S. A. Mohammed, et al., Complex and real optical soliton properties of the paraxial non-linear Schrödinger equation in Kerr media with M-Fractional, Front. Phys., 7 (2019), 197. Doi: 10.3389/fphy.2019.00197.
    [46] A. Abdel-Aty, N. Zakaria, L. Y. Cheong, et al., Effect of the Spin-Orbit interaction on partial entangled quantum network, Lect. Notes Elect. Eng., 285 (2014), 529-237. doi: 10.1007/978-981-4585-18-7_59
    [47] M. Zidan, A. Abdel-Aty, A. Younes, et al., A novel algorithm based on entanglement measurement for improving speed of quantum algorithms, Appl. Math. Inf. Sci., 12 (2018), 265-269. doi: 10.18576/amis/120127
    [48] S. Owyed, M. A. Abdou, A. Abdel-Aty, et al., New optical soliton solutions of nonlinear evolution equation describing nonlinear dispersion, Commun. Theor. Phys., 71 (2019), 1063-1068. doi: 10.1088/0253-6102/71/9/1063
    [49] A. Abdel-Aty, N. Zakaria, L. Y. Cheong, et al., Entanglement and teleportation via partial entangled-state quantum network, J. Comput. Theor. Nanosci., 12 (2015), 2213-2220. doi: 10.1166/jctn.2015.4010
    [50] M. Abdel-Aty, General formalism of interaction of a two-level atom with cavity field in arbitrary forms of nonlinearities, Physica A., 313 (2002), 471-487. doi: 10.1016/S0378-4371(02)00999-8
    [51] A. Abdel-Aty, N. Zakaria, L. Y. Cheong, et al., Quantum network via partial entangled state, J. Commun., 9 (2014), 379-384.
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