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Optical and Quantum Electronics

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01.01.2022

Analytical solutions to the fractional Lakshmanan–Porsezian–Daniel model

verfasst von: H. Yépez-Martínez, Hadi Rezazadeh, Mustafa Inc, Mehmet Ali Akinlar, J. F. Gómez-Aguilar

Erschienen in: Optical and Quantum Electronics | Ausgabe 1/2022

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Abstract

A new local fractional-order derivative operator is introduced and the Lakshmanan–Porsezian–Daniel (LPD) model is interpreted via this operator. New analytical solutions to the LPD equation is presented by Jacobi elliptic functions and an anzätz method. The complex-valued LPD equation includes a nonlinear term which is considered from three different cases: Kerr, parabolic and anti-cubic law of nonlinearities. For each case, dark, bright, singular optical soliton solutions related with optical fibers are presented. Simulations representing behavior of these solutions for different parameter values are provided.

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Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)MathSciNetMATHCrossRef

Akbar, L., Akinyemi, M.A., Yao, S.-W., Jhangeer, A., Rezazadeh, H., Khater, M.M.A., Ahmad, H., Inc, M.: Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method. Results Phys. 25, 104228 (2021)CrossRef

Akinyemi, L.: Two improved techniques for the perturbed nonlinear Biswas–Milovic equation and its optical solitons. Optik 243, 167477 (2021)ADSCrossRef

Akinyemi, L., Hosseini, K., Salahshour, S.: The bright and singular solitons of (2+1)-dimensional nonlinear Schrödinger equation with spatio-temporal dispersions. Optik 242, 167120 (2021a)ADSCrossRef

Akinyemi, L., Rezazadeh, H., Yao, S.-W., Akbar, M.A., Khater, M.M.A., Jhangeer, A., Inc, M., Ahmad, H.: Nonlinear dispersion in parabolic law medium and its optical solitons. Results Phys. 26, 104411 (2021b)CrossRef

Akinyemi, L., Şenol, M., Osman, M.S.: Analytical and approximate solutions of nonlinear Schrödinger equation with higher dimension in the anomalous dispersion regime. J. Ocean Eng. Sci. (2021c). https://doi.org/10.1016/j.joes.2021.07.006CrossRef

Akram, G., Sadaf, M., Dawood, M., Baleanu, D.: Optical solitons for Lakshmanan–Porsezian–Daniel equation with Kerr law non-linearity using improved \(tan \left(\dfrac{\psi (\eta )}{2} \right)\)-expansion technique. Results Phys. 29, 104758 (2021)CrossRef

Almeida, R., Guzowska, M., Odzijewicz, T.: A remark on local fractional calculus and ordinary derivatives. Open Math. 14, 1122–1124 (2016)MathSciNetMATHCrossRef

Arshed, S., Biswas, A., Majid, F.B., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical solitons in birefringent fibers for Lakshmanan–Porsezian–Daniel model using \(exp(-\phi ( ))\)-expansion method. Optik 168, 555–560 (2018)ADSCrossRef

Aslan, E.C., Tchier, F., Inc, M.: On optical solitons of the Schrödinger–Hirota equation with power law nonlinearity in optical fibers. Superlattices Microstruct. 105, 48–55 (2017)ADSCrossRef

Atangana, A., Baleanu, D.: New fractional derivatives with nonlocal and non-singular kernel. Theory and application to heat transfer model. Therm. Sci. 20(2), 763–769 (2016)CrossRef

Atangana, A., Secer, A.: A note on fractional order derivatives and table of fractional derivatives of some special functions. Abstr. Appl. Anal. 2013, 279681 (2013)MathSciNetMATHCrossRef

Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Manrakhan, W.N., Savescu, M., Biswas, A.: Dispersive optical solitons with Schrödinger–Hirota equation. J. Nonlinear Opt. Phys. Mater. 23(1), 1–21 (2014). https://doi.org/10.1142/S0218863514500143CrossRef

Biswas, A.: Solitary wave solution for KdV equation with power-law nonlinearity and time-dependent coefficients. Nonlinear Dyn. 58(1–2), 345–348 (2009)MathSciNetMATHCrossRef

Biswas, A.: Solitary waves for power-law regularized long-wave equation and \({R}(m, n)\) equation. Nonlinear Dyn. 59(3), 423–426 (2010)MathSciNetMATHCrossRef

Biswas, A., Konar, A.: Introduction to Non-Kerr Law Optical Solitons. CRC Press, Boca Raton (2006)MATHCrossRef

Biswas, A., Yıldırım, Y., Yaşar, E., Alqahtani, R.T.: Optical solitons for Lakshmanan–Porsezian–Daniel model with dual-dispersion by trial equation method. Optik 168, 432–439 (2018a)ADSCrossRef

Biswas, A., Yıldırım, Y., Yaşar, E., Zhou, Q., Moshokoac, S.P., Belic, M.: Optical solitons for Lakshmanan–Porsezian–Daniel model by modified simple equation method. Optik 160, 24–32 (2018)ADSCrossRef

Caputo, M., Fabricio, M.: A new definition of fractional derivative without singular kernel. Prog. Fract. Differ. Appl. 1(2), 73–85 (2015)

Caputo, M., Mainardi, F.: A new dissipation model based on memory mechanism. Pure Appl. Geophys. 91, 134–147 (1971)ADSMATHCrossRef

Dai, C.Q., Wang, Y.Y., Fan, Y., Yu, D.G.: Reconstruction of stability for Gaussian spatial solitons in quintic-septimal nonlinear materials under \({{{\cal{P}}}}{{\cal{T}}}\)-symmetric potentials. Nonlinear Dyn. 92(3), 1351–1358 (2018)CrossRef

Dowluru, R.K., Bhima, P.R.: Influences of third order dispersion on linear birefringent optical soliton transmission systems. J. Opt. 40(3), 132–142 (2011)CrossRef

El, G.A., Geogjaev, V.V., Gurevich, A.V., Krylov, A.L.: Decay of an initial discontinuity in the defocusing NLS hydrodynamics. Physica D 87(1–4), 186–192 (1995)ADSMathSciNetMATHCrossRef

Fandio-Jubgang, D., Dikandé, A.M., Sunda-Meya, A.: Elliptic solitons in optical fiber media. Phys. Rev. A 92(5), 1–7 (2015). https://doi.org/10.1103/PhysRevA.92.053850CrossRef

Fujioka, J.E., Cortés, E., Pérez-Pascual, R., Rodríguez, R.F., Espinosa, A., Malomed, B.A.: Chaotic solitons in the quadratic-cubic nonlinear Schrödinger equation under nonlinearity management. Chaos Interdiscip. J. Nonlinear Sci. 21(3), 033120 (2011)MATHCrossRef

Green, P., Biswas, A.: Bright and dark optical solitons with time-dependent coefficients in a non-Kerr law media. Commun. Nonlinear Sci. Numer. Simul. 15(12), 3865–3873 (2010)ADSMathSciNetMATHCrossRef

Guzman, P.M., Langton, G., Motta Bittencurt, L.M.L., Medina, J., Napoles-Valdes, J.E.: A new definition of a fractional derivative of local type. J. Math. Anal. 9(2), 88–98 (2018)MathSciNet

Inc, M.: Some special structures for the generalized Nonlinear Schrödinger equation with nonlinear dispersion. Waves Random Complex Media 23(2), 77–88 (2013)ADSMathSciNetCrossRef

Inc, M., Ates, E.: Optical soliton solutions for generalized NLSE by using Jacobi elliptic functions. Optoelectron. Adv. Mater. Rapid Commun. 9, 1081–1087 (2015)

Inc, M., Ulutas, E., Cavlak, E., Biswas, A.: Singular 1-soliton solution of the \({K}(m, n)\) equation with generalized evolutions and its subsidiaries. Acta Phys. Pol. B 44(9), 1825–1836 (2013)ADSMathSciNetMATHCrossRef

Ivanov, S.K.: Riemann problem for the light pulses in optical fibers for the generalized Chen–Lee–Liu equation. Phys. Rev. A 101(5), 053827 (2020)ADSMathSciNetCrossRef

Kilic, B., Inc, M.: On optical solitons of the resonant Schrödingers equation in optical fibers with dual-power law nonlinearity and time-dependent coefcients. Waves Random Complex Media 25, 245–251 (2015)MATHCrossRef

Lakshmanan, M., Porsezian, K., Daniel, M.: Effect of discreteness on the continuum limit of the Heisenberg spin chain. Phys. Lett. A 133(9), 483–488 (1998)ADSCrossRef

Liu, W., Liu, M., OuYang, Y., Hou, H., Ma, G., Lei, M., Wei, Z.: Tungsten diselenide for mode-locked erbium-doped fiber lasers with short pulse duration. Nanotechnology 29(17), 1–8 (2018)CrossRef

Liu, W., Zhu, Y.N., Liu, M., Wen, B., Fang, S., Teng, H., Wei, Z.: Optical properties and applications for \(mos_2\)-\(sb_2 te_3\)-\(mos_2\) heterostructure materials. Photonics Res. 6(3), 220–227 (2018)CrossRef

Miller, K.S., Ross, B.: TAn Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)MATH

Mirzazadeh, M., Arnous, A.H., Mahmood, M.F., Zerrad, E., Biswas, A.: Soliton solutions to resonant nonlinear Schrödinger’s equation with time-dependent coefficients by trial solution approach. Nonlinear Dyn. 81(1–2), 277–282 (2015)MATHCrossRef

Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, London (1974)MATH

Rasheed, N.M., Al-Amr, M.O., Az-Zo’bi, M.A., Tashtoush, E.A., Akinyemi, L.: Stable optical solitons for the higher-order non-Kerr NLSE via the modified simple equation method. Mathematics 9(16), 1986 (2021). https://doi.org/10.3390/math9161986CrossRef

Rezazadeh, H., Mirzazadeh, M., Mirhosseini-Alizamini, S.M., Neirameh, A., Eslami, M., Zhou, Q.: Optical solitons of Lakshmanan–Porsezian–Daniel model with a couple of nonlinearities. Optik 164, 414–423 (2018)ADSCrossRef

Sirisubtawee, S.S., Koonprasert, S., Sungnul, S.: Some applications of the \((g^{\prime }/g, 1/g)\)-expansion method for finding exact traveling wave solutions of nonlinear fractional evolution equations. Symmetry 11(8), 952 (2019)CrossRef

Sassaman, R., Biswas, A.: Topological and nontopological solitons of the Klein–Gordon equations in \(1+2\) dimensions. Nonlinear Dyn. 61(1–2), 23–28 (2010)MATHCrossRef

Seadawy, A.R., Dianchen, L.D., Nasreen, N., Nasreen, S.: Structure of optical solitons of resonant Schrödinger equation with quadratic cubic nonlinearity and modulation instability analysis. Physica A 534(3), 122155 (2019)MathSciNetCrossRef

Sousa, J.V.D.C., de Oliveira, E.C.: A new truncated \(m\)-fractional derivative type unifying some fractional derivative types with classical properties. Int. J. Anal. Appl. 16(1), 83–96 (2018)MATH

Vega-Guzman, J., Biswas, A., Mahmood, M.F., Zhou, Q., Moshokoa, S.P., Belic, M.R.: Optical solitons with polarization mode dispersion for Lakshmanan–Porsezian–Daniel model by the method of undetermined coefficients. Optik 171, 114–119 (2018)ADSCrossRef

Wang, Y.Y., Dai, C.Q., Xu, Y.Q., Zheng, J., Fan, Y.: Dynamics of nonlocal and localized spatiotemporal solitons for a partially nonlocal nonlinear Schrödinger equation. Nonlinear Dyn. 92(3), 1261–1269 (2010)CrossRef

Wang, Y.Y., Chen, L., Dai, C.Q., Zheng, J., Fan, Y.: Exact vector multipole and vortex solitons in the media with spatially modulated cubic-quintic nonlinearity. Nonlinear Dyn. 90(2), 1269–1275 (2017)MathSciNetCrossRef

Yaşar, E., Yıldırım, Y., Yaşar, E.: New optical solitons of space-time conformable fractional perturbed Gerdjikov–Ivanov equation by sine-Gordon equation method. Results Phys. 9, 1666–1672 (2018)ADSCrossRef

Ye, Y.L., Hou, D.D., Cheng, C., Chen, S.H.: Rogue wave solutions of the vector Lakshmanan–Porsezian–Daniel equation. Phys. Lett. A 384(11), 126226 (2020). https://doi.org/10.1016/j.physleta.2019.126226MathSciNetCrossRefMATH

Yépez-Martínez, H., Gómez-Aguilar, J.F.: M-derivative applied to the soliton solutions for the Lakshmanan–Porsezian–Daniel equation with dual-dispersion for optical fibers. Opt. Quantum Electron. 51, 31 (2019). https://doi.org/10.1007/s11082-018-1740-5CrossRef

Yépez-Martínez, H., Gómez-Aguilar, J.F.: Optical solitons solution of resonance nonlinear Schrödinger type equation with Atangana’s-conformable derivative using sub-equation method. Waves Random Complex Media 31(3), 573–596 (2021)ADSMathSciNetCrossRef

Yépez-Martínez, H., Gómez-Aguilar, J.F., Baleanu, D.: Beta-derivative and sub-equation method applied to the optical solitons in medium with parabolic law nonlinearity and higher order dispersion. Optik 155, 357–365 (2018)ADSCrossRef

Yépez-Martínez, H., Rezazadeh, H., Inc, M., Akinlar, M.A.: New solutions to the fractional perturbed Chen–Lee–Liu equation with a new local fractional derivative. In: Waves in Random and Complex Media, pp. 1–36 (2021). https://doi.org/10.1080/17455030.2021.1930280

Yıldırım, Y., Topkara, E., Biswas, A., Triki, H., Ekici, M., Guggilla, P., Khan, S., Belic, M.R.: Cubic-quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by sine-Gordon equation approach. J. Opt. 50(2), 322–329 (2021)CrossRef

Zakharov, V.E., Shabat, A.B.: Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34(1), 62–69 (1972)ADSMathSciNet

Zhang, Z.Y., Liu, Z.H., Miao, X.J., Chen, Y.Z.: New exact solutions to the perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity. Appl. Math. Comput. 216, 3064–3072 (2010)MathSciNetMATH

Titel: Analytical solutions to the fractional Lakshmanan–Porsezian–Daniel model
verfasst von: H. Yépez-Martínez
Hadi Rezazadeh
Mustafa Inc
Mehmet Ali Akinlar
J. F. Gómez-Aguilar
Publikationsdatum: 01.01.2022
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 1/2022
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-021-03378-w

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