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Erschienen in: Optical and Quantum Electronics 4/2019

01.04.2019

Optical solitons in nematic liquid crystals with Kerr and parabolic law nonlinearities

verfasst von: Nauman Raza, Usman Afzal, Asma Rashid Butt, Hadi Rezazadeh

Erschienen in: Optical and Quantum Electronics | Ausgabe 4/2019

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Abstract

In this work, a study is carried out to analyze nematicons in liquid crystals in the presence of Kerr and parabolic law nonlinearity. Exp(−\(\phi ({\xi })\))-Expansion method is incorporated in this regard. Solutions obtained include hyperbolic, periodic and rational solutions along with their combo type solutions in both cases of nonlinearity and their existence is guaranteed by the constraints retrieved during the process.

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Literatur
Zurück zum Zitat Akbar, M.A., Ali, N.H.M.: Exp-function method for Duffing equation and new solutions of (2+1)-dimensional dispersive long wave equations. Prog. Appl. Math. 1(2), 30–42 (2011) Akbar, M.A., Ali, N.H.M.: Exp-function method for Duffing equation and new solutions of (2+1)-dimensional dispersive long wave equations. Prog. Appl. Math. 1(2), 30–42 (2011)
Zurück zum Zitat Arnous, A.H., Zaka Ullah, M., Asma, M., Moshokoa, S.P., Mirzazadeh, M., Biswas, A., Belic, M.: Nematicons in liquid crystals by modified simple equation method. Nonlinear Dyn. 88, 2863–2872 (2017)MathSciNetCrossRef Arnous, A.H., Zaka Ullah, M., Asma, M., Moshokoa, S.P., Mirzazadeh, M., Biswas, A., Belic, M.: Nematicons in liquid crystals by modified simple equation method. Nonlinear Dyn. 88, 2863–2872 (2017)MathSciNetCrossRef
Zurück zum Zitat Assanto, G.: Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals. Wiley, New York (2012)CrossRef Assanto, G.: Nematicons: Spatial Optical Solitons in Nematic Liquid Crystals. Wiley, New York (2012)CrossRef
Zurück zum Zitat Assanto, G., Karpierz, M.: Nematicons: self-localized beams in nematic liquid crystals. Liq. Cryst. 36, 1161–1172 (2009)CrossRef Assanto, G., Karpierz, M.: Nematicons: self-localized beams in nematic liquid crystals. Liq. Cryst. 36, 1161–1172 (2009)CrossRef
Zurück zum Zitat Biswas, A., Al-Amr, M.O., Rezazadeh, H., Mirzazadeh, M., Eslami, M., Zhou, Q., Moshokoa, S.P., Belic, M.: Resonant optical solitons with dual-power law nonlinearity and fractional temporal evolution. Optik 165, 233–239 (2018)ADSCrossRef Biswas, A., Al-Amr, M.O., Rezazadeh, H., Mirzazadeh, M., Eslami, M., Zhou, Q., Moshokoa, S.P., Belic, M.: Resonant optical solitons with dual-power law nonlinearity and fractional temporal evolution. Optik 165, 233–239 (2018)ADSCrossRef
Zurück zum Zitat Bulut, H., Sulaiman, T.A., Baskonus, H.M., Rezazadeh, H., Eslami, M., Mirzazadeh, M.: Optical solitons and other solutions to the conformable space–time fractional Fokas–Lenells equation. Optik 172, 20–27 (2018)ADSCrossRef Bulut, H., Sulaiman, T.A., Baskonus, H.M., Rezazadeh, H., Eslami, M., Mirzazadeh, M.: Optical solitons and other solutions to the conformable space–time fractional Fokas–Lenells equation. Optik 172, 20–27 (2018)ADSCrossRef
Zurück zum Zitat Conti, C., Peccianti, M., Assanto, G.: Observation of optical spatial solitons in a highly nonlocal medium. Phys. Rev. Lett. 92, 113–902 (2004) Conti, C., Peccianti, M., Assanto, G.: Observation of optical spatial solitons in a highly nonlocal medium. Phys. Rev. Lett. 92, 113–902 (2004)
Zurück zum Zitat Ebaid, A.: An improvement on the Exp-function method when balancing the highest order linear and nonlinear terms. J. Math. Anal. Appl. 392(1), 1–5 (2012)MathSciNetMATHCrossRef Ebaid, A.: An improvement on the Exp-function method when balancing the highest order linear and nonlinear terms. J. Math. Anal. Appl. 392(1), 1–5 (2012)MathSciNetMATHCrossRef
Zurück zum Zitat Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Ullah, M.Z., Zhou, Q., Triki, H., Moshokoa, S.P., Biswas, A.: Optical solitons with anti-cubic nonlinearity by extended trial equation method. Optik 136, 368–373 (2017a)ADSCrossRef Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Ullah, M.Z., Zhou, Q., Triki, H., Moshokoa, S.P., Biswas, A.: Optical solitons with anti-cubic nonlinearity by extended trial equation method. Optik 136, 368–373 (2017a)ADSCrossRef
Zurück zum Zitat Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Ullah, M.Z., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Nematicons in liquid crystals by extended trial equation method. J. Nonlinear Opt. Phys. Mater. 26, 1750005 (2017b)ADSCrossRef Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Ullah, M.Z., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Nematicons in liquid crystals by extended trial equation method. J. Nonlinear Opt. Phys. Mater. 26, 1750005 (2017b)ADSCrossRef
Zurück zum Zitat Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Zhou, Q., Triki, H., Ullah, M.Z., Moshokoa, S.P., Biswas, A.: Optical solitons in birefringent fibers with Kerr nonlinearity by Exp-function method. Optik 131, 964–976 (2017c)ADSCrossRef Ekici, M., Mirzazadeh, M., Sonmezoglu, A., Zhou, Q., Triki, H., Ullah, M.Z., Moshokoa, S.P., Biswas, A.: Optical solitons in birefringent fibers with Kerr nonlinearity by Exp-function method. Optik 131, 964–976 (2017c)ADSCrossRef
Zurück zum Zitat Garcìa-Reimbert, C., Minzoni, A.A., Smyth, N.F.: Spatial soliton evolution in nematic liquid crystals in the nonlinear local regime. J. Opt. Soc. Am. B 23, 294–301 (2006a)ADSCrossRef Garcìa-Reimbert, C., Minzoni, A.A., Smyth, N.F.: Spatial soliton evolution in nematic liquid crystals in the nonlinear local regime. J. Opt. Soc. Am. B 23, 294–301 (2006a)ADSCrossRef
Zurück zum Zitat Garcìa-Reimbert, C., Minzoni, A.A., Smyth, N.F., Worthy, A.L.: Large-amplitude nematicon propagation in a liquid crystal with local response. J. Opt. Soc. Am. B 23, 2551–2558 (2006b)ADSCrossRef Garcìa-Reimbert, C., Minzoni, A.A., Smyth, N.F., Worthy, A.L.: Large-amplitude nematicon propagation in a liquid crystal with local response. J. Opt. Soc. Am. B 23, 2551–2558 (2006b)ADSCrossRef
Zurück zum Zitat He, J.H., Abdou, M.A.: New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos Solitons Fractals 34(5), 1421–1429 (2007)ADSMathSciNetMATHCrossRef He, J.H., Abdou, M.A.: New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos Solitons Fractals 34(5), 1421–1429 (2007)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Javid, A., Raza, N.: Singular and dark optical solitons to the well posed Lakshamanan–Porsezian–Daniel model. Optik 171, 120–129 (2018)ADSCrossRef Javid, A., Raza, N.: Singular and dark optical solitons to the well posed Lakshamanan–Porsezian–Daniel model. Optik 171, 120–129 (2018)ADSCrossRef
Zurück zum Zitat Kavitha, L., Venkatesh, M., Dhamayanthi, S., Gopi, D.: Nonlinear refractive index induced collision and propagation of nematicons. J. Mol. Liq. 197, 142–151 (2014)CrossRef Kavitha, L., Venkatesh, M., Dhamayanthi, S., Gopi, D.: Nonlinear refractive index induced collision and propagation of nematicons. J. Mol. Liq. 197, 142–151 (2014)CrossRef
Zurück zum Zitat Kavitha, L., Venkatesh, M., Dhamayanthi, S., Gopi, D.: Modulational instability of optically induced nematicon propagation. Chin. Phys. B 22(12), 129–401 (2013)CrossRef Kavitha, L., Venkatesh, M., Dhamayanthi, S., Gopi, D.: Modulational instability of optically induced nematicon propagation. Chin. Phys. B 22(12), 129–401 (2013)CrossRef
Zurück zum Zitat Khan, K., Akbar, M.A.: The Exp(−\(\phi ({\xi })\))-Expansion method for finding travelling wave solutions of Vakhnenko–Parkes equation. Int. J. Dyn. Syst. Differ. Equ. 5(1), 72–83 (2014)MathSciNetMATH Khan, K., Akbar, M.A.: The Exp(−\(\phi ({\xi })\))-Expansion method for finding travelling wave solutions of Vakhnenko–Parkes equation. Int. J. Dyn. Syst. Differ. Equ. 5(1), 72–83 (2014)MathSciNetMATH
Zurück zum Zitat Khoo, I.C., Wu, N.T.: Optics and Nonlinear Optics of Liquid Crystals. World Scientific Publishing, Singapore (1993)CrossRef Khoo, I.C., Wu, N.T.: Optics and Nonlinear Optics of Liquid Crystals. World Scientific Publishing, Singapore (1993)CrossRef
Zurück zum Zitat Liu, X., Triki, H., Zhou, Q., Mirzazadeh, M., Liu, W., Biswas, A., Belic, M.: Generation and control of multiple solitons under the influence of parameters. Nonlinear Dyn. 95, 143–150 (2019a)CrossRef Liu, X., Triki, H., Zhou, Q., Mirzazadeh, M., Liu, W., Biswas, A., Belic, M.: Generation and control of multiple solitons under the influence of parameters. Nonlinear Dyn. 95, 143–150 (2019a)CrossRef
Zurück zum Zitat Liu, W., Zhang, Y., Triki, H., Mirzazadeh, M., Ekici, M., Zhou, Q., Biswas, A., Belic, M.: Interaction properties of solitonics in inhomogeneous optical fibers. Nonlinear Dyn. 95, 557–563 (2019b)CrossRef Liu, W., Zhang, Y., Triki, H., Mirzazadeh, M., Ekici, M., Zhou, Q., Biswas, A., Belic, M.: Interaction properties of solitonics in inhomogeneous optical fibers. Nonlinear Dyn. 95, 557–563 (2019b)CrossRef
Zurück zum Zitat Minzoni, A.A., Smyth, N.F., Worthy, A.L.: Modulation solutions for nematicon propagation in non-local liquid crystals. J. Opt. Soc. Am. B 24, 1549–1556 (2007)ADSCrossRef Minzoni, A.A., Smyth, N.F., Worthy, A.L.: Modulation solutions for nematicon propagation in non-local liquid crystals. J. Opt. Soc. Am. B 24, 1549–1556 (2007)ADSCrossRef
Zurück zum Zitat Navickas, Z., Ragulskis, M., Bikulciene, L.: Be careful with the Exp-function method-additional remarks. Commun. Nonlinear Sci. Numer. Simul. 15, 3874–3886 (2010)ADSMathSciNetMATHCrossRef Navickas, Z., Ragulskis, M., Bikulciene, L.: Be careful with the Exp-function method-additional remarks. Commun. Nonlinear Sci. Numer. Simul. 15, 3874–3886 (2010)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Noor, M.A., Mohyud-Din, S.D., Waheed, A.: Exp-function method for generalized traveling solutions of master partial differential equation. Acta Appl. Math. 104(2), 131–137 (2008)MathSciNetMATHCrossRef Noor, M.A., Mohyud-Din, S.D., Waheed, A.: Exp-function method for generalized traveling solutions of master partial differential equation. Acta Appl. Math. 104(2), 131–137 (2008)MathSciNetMATHCrossRef
Zurück zum Zitat Ravi, L.K., Saha Ray, S., Sahoo, S.: New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method. J. Ocean Eng. Sci. 2, 34–46 (2017)CrossRef Ravi, L.K., Saha Ray, S., Sahoo, S.: New exact solutions of coupled Boussinesq–Burgers equations by Exp-function method. J. Ocean Eng. Sci. 2, 34–46 (2017)CrossRef
Zurück zum Zitat Raza, N., Javid, A.: Optical dark and singular solitons to the Biswas–Milovic equation in nonlinear optics with spatio-temporal dispersion. Optik 158, 1057–1094 (2018b)ADSCrossRef Raza, N., Javid, A.: Optical dark and singular solitons to the Biswas–Milovic equation in nonlinear optics with spatio-temporal dispersion. Optik 158, 1057–1094 (2018b)ADSCrossRef
Zurück zum Zitat Raza, N., Zubair, A.: Bright, dark and dark-singular soliton solutions of nonlinear Schrodinger’s equation with spatio-temporal dispersion. J. Mod. Opt. 65, 1975–1982 (2018)ADSMathSciNetCrossRef Raza, N., Zubair, A.: Bright, dark and dark-singular soliton solutions of nonlinear Schrodinger’s equation with spatio-temporal dispersion. J. Mod. Opt. 65, 1975–1982 (2018)ADSMathSciNetCrossRef
Zurück zum Zitat Rezazadeh, H., Alizamini, S.M.M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger–Hirota equation. Optik 172, 545–553 (2018a)ADSCrossRef Rezazadeh, H., Alizamini, S.M.M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger–Hirota equation. Optik 172, 545–553 (2018a)ADSCrossRef
Zurück zum Zitat Rezazadeh, H., Tariq, H., Eslami, M., Mirzazadeh, M., Zhou, Q.: New exact solutions of nonlinear conformable time-fractional Phi-4 equation. Chin. J. Phys. 56, 2805–2816 (2018b)CrossRef Rezazadeh, H., Tariq, H., Eslami, M., Mirzazadeh, M., Zhou, Q.: New exact solutions of nonlinear conformable time-fractional Phi-4 equation. Chin. J. Phys. 56, 2805–2816 (2018b)CrossRef
Zurück zum Zitat Savescu, M., Johnson, S., Sanchez, P., Zhou, Q., Mahmood, M.F., Zerrad, E., Biswas, A., Belic, M.: Nematicons in liquid crystals. J. Comput. Theor. Nanosci. 12, 4667–4673 (2015)CrossRef Savescu, M., Johnson, S., Sanchez, P., Zhou, Q., Mahmood, M.F., Zerrad, E., Biswas, A., Belic, M.: Nematicons in liquid crystals. J. Comput. Theor. Nanosci. 12, 4667–4673 (2015)CrossRef
Zurück zum Zitat Sciberras, L.W., Minzoni, A.A., Smyth, N.F., Assanto, G.: Steering of optical solitary waves by coplanar low power beams in reorientational media. J. Nonlinear Opt. Phys. Mater. 23(4), 1450045 (2014)ADSCrossRef Sciberras, L.W., Minzoni, A.A., Smyth, N.F., Assanto, G.: Steering of optical solitary waves by coplanar low power beams in reorientational media. J. Nonlinear Opt. Phys. Mater. 23(4), 1450045 (2014)ADSCrossRef
Zurück zum Zitat Simoni, F.: Nonlinear Optical Properties of Liquid Crystals. World Scientific Publishing, London (1997)CrossRef Simoni, F.: Nonlinear Optical Properties of Liquid Crystals. World Scientific Publishing, London (1997)CrossRef
Zurück zum Zitat Tabiryan, N.V., Sukhov, A.V., Zel’dovich, B.Y.A.: Orientational optical nonlinearity of liquid crystals. Mol. Cryst. Liq. Cryst. 136, 1–139 (1986)CrossRef Tabiryan, N.V., Sukhov, A.V., Zel’dovich, B.Y.A.: Orientational optical nonlinearity of liquid crystals. Mol. Cryst. Liq. Cryst. 136, 1–139 (1986)CrossRef
Zurück zum Zitat Yang, C., Zhou, Q., Triki, H., Mirzazadeh, M., Ekici, M., Liu, W., Biswas, A., Belic, M.: Bright soliton interactions in a (2 + 1)-dimensional fourth-order variable-coefficient nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain. Nonlinear Dyn. (2018). https://doi.org/10.1007/s11071-018-4609-z CrossRef Yang, C., Zhou, Q., Triki, H., Mirzazadeh, M., Ekici, M., Liu, W., Biswas, A., Belic, M.: Bright soliton interactions in a (2 + 1)-dimensional fourth-order variable-coefficient nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain. Nonlinear Dyn. (2018). https://​doi.​org/​10.​1007/​s11071-018-4609-z CrossRef
Zurück zum Zitat Yu, W., Ekici, M., Mirzazadeh, M., Zhou, Q., Liu, W.: Periodic oscillations of dark solitons in nonlinear optics. Optik 165, 341–344 (2018)ADSCrossRef Yu, W., Ekici, M., Mirzazadeh, M., Zhou, Q., Liu, W.: Periodic oscillations of dark solitons in nonlinear optics. Optik 165, 341–344 (2018)ADSCrossRef
Zurück zum Zitat Yu, W., Zhou, Q., Mirzazadeh, M., Liu, W., Biswas, A.: Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics. J. Adv. Res. 15, 69–76 (2019)CrossRef Yu, W., Zhou, Q., Mirzazadeh, M., Liu, W., Biswas, A.: Phase shift, amplification, oscillation and attenuation of solitons in nonlinear optics. J. Adv. Res. 15, 69–76 (2019)CrossRef
Zurück zum Zitat Zhang, Y., Yang, C., Yu, W., Mirzazadeh, M., Zhou, Q., Liu, W.: Interactions of vector anti-dark solitons for the coupled nonlinear Schrödinger equation in inhomogeneous fibers. Nonlinear Dyn. 94, 1351–1360 (2018)CrossRef Zhang, Y., Yang, C., Yu, W., Mirzazadeh, M., Zhou, Q., Liu, W.: Interactions of vector anti-dark solitons for the coupled nonlinear Schrödinger equation in inhomogeneous fibers. Nonlinear Dyn. 94, 1351–1360 (2018)CrossRef
Zurück zum Zitat Zhou, Q., Yao, D., Chen, F.: Analytical study of optical solitons in media with Kerr and parabolic law nonlinearities. J. Mod. Opt. 60(19), 1652–1657 (2013)ADSCrossRef Zhou, Q., Yao, D., Chen, F.: Analytical study of optical solitons in media with Kerr and parabolic law nonlinearities. J. Mod. Opt. 60(19), 1652–1657 (2013)ADSCrossRef
Zurück zum Zitat Zhou, Q., Pan, A., Rezazadeh, H., Mirzazadeh, M., Moosavi, S.S., Eslami, M., Ekici, M., Liu, W.: Exact solutions of the perturbed modified KdV equation using the functional variable method. J. Optoelectron. Adv. Mater. 20, 279–284 (2018) Zhou, Q., Pan, A., Rezazadeh, H., Mirzazadeh, M., Moosavi, S.S., Eslami, M., Ekici, M., Liu, W.: Exact solutions of the perturbed modified KdV equation using the functional variable method. J. Optoelectron. Adv. Mater. 20, 279–284 (2018)
Zurück zum Zitat Zubair, A., Raza, N., Mirzazadeh, M., Liu, W., Zhou, Q.: Analytic study on optical solitons in parity-time-symmetric mixed linear and nonlinear modulation lattices with non-Kerr nonlinearities. Optik 173, 249–262 (2018)ADSCrossRef Zubair, A., Raza, N., Mirzazadeh, M., Liu, W., Zhou, Q.: Analytic study on optical solitons in parity-time-symmetric mixed linear and nonlinear modulation lattices with non-Kerr nonlinearities. Optik 173, 249–262 (2018)ADSCrossRef
Metadaten
Titel
Optical solitons in nematic liquid crystals with Kerr and parabolic law nonlinearities
verfasst von
Nauman Raza
Usman Afzal
Asma Rashid Butt
Hadi Rezazadeh
Publikationsdatum
01.04.2019
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 4/2019
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-019-1813-0

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