Abstract
This analysis utilizes the generalized Riccati simple equation method to construct nematicons in liquid crystals from its governing system. A new type of nonlinearity is studied for the first time in the context of liquid crystals. It is the nonlinear quadruple power law. The fractional version of the governed model, with conformable sense, is considered. With the aid of Mathematica, Bright, dark, and singular types of solutions are derived with the constraints guaranteeing their existence. Moreover, some obtained results are depicted to show the real physical characteristics of nematicons. The used method provides a powerful tool for extracting exact solitary wave solutions. By simple calculations, we show that the generalized Riccati simple equation method can be treated as a general case of the well-known simple equation, \(\exp \left( -\varphi (\eta )\right)\)-expansion, and \(\left( {G}^{\prime }/G\right)\)-expansion methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Availability of data and materials
Not applicable.
References
Abdeljawad, T.: On conformable fractional calculus. J. Comput. Appl. Math. 279, 57–66 (2015)
Akçağıl, Ş: On the relations between some well-known methods and the projective Riccati equations. Open Phys. 18(1), 613–618 (2020). https://doi.org/10.1515/phys-2020-0124
Akinyemi, L., Senol, M., Az-Zo’Bi, E., Veeresha, P., Akpan, U.: Novel soliton solutions of four sets of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili-like equations. Mod. Phys. Lett. B 36(1), 2150530 (2022)
Alberucci, A., Assanto, G.: Dissipative self-confined optical beams in doped nematic liquid crystals. J. Nonlinear Opt. Phys. Mater. 16(3), 295–305 (2007)
Assanto, G., Karpierz, M.: Nematicons: self-localized beams in nematic liquid crystals. Liq. Cryst. 36, 1161–1172 (2009)
Assanto, G., Peccianti, M., Conti, C.: Nematicons: optical spatial solitons in nematic liquid crystals. Opt. Photon-News 14, 44–48 (2003)
Assanto, G., Fratalocchi, A., Peccianti, M.: Spatial solitons in nematic liquid crystals. Opt. Exp. 15, 5248–5259 (2007)
Assanto, G., Skuse, B.D., Smyth, N.F.: Optical path control of solitary waves in dye-doped nematic liquid crystals. Photonics Lett. Pol. 1(4), 154–156 (2009). https://doi.org/10.4302/photon.lett.pl.v1i4.65
Assanto, G., Smyth, N.F., Xia, W.: Refraction of nonlinear light beams in nematic liquid crystals. J. Nonlinear Opt. Phys. Mater. 21(3), 1250033 (2012)
Az-Zo’bi, E.A.: New kink solutions for the van der Waals p-system. Math. Methods Appl. Sci. 42(18), 6216–6226 (2019a)
Az-Zo’bi, E.A.: Peakon and solitary wave solutions for the modified Fornberg–Whitham equation using simplest equation method. Int. J. Math. Comput. Sci. 14(3), 635–645 (2019b)
Az-Zo’bi, E.A., Akinyemi, L., Alledawi, A.O.: Construction of optical solitons for conformable generalized model in nonlinear media. Mod. Phys. Lett. B (2021a). https://doi.org/10.1142/S0217984921504091
Az-Zo’bi, E.A., Alzoubi, W.A., Akinyemi, L., Şenol, M., Masaedeh, B.S.: A variety of wave amplitudes for the conformable fractional (2+1)-dimensional Ito equation. Mod. Phys. Lett. B (2021b). https://doi.org/10.1142/S0217984921502547
Az-Zo’bi, E.A., AlZoubi, W.A., Akinyemi, L., Şenol, M., Alsaraireh, I.W., Mamat, M.: Abundant closed-form solitons for time-fractional integro-differential equation in fluid dynamics. Opt. Quantum Electron. 53, 132 (2021c). https://doi.org/10.1007/s11082-021-02782-6
Baskonus, H.M., Sulaiman, T.A., Bulut, H.: Dark, bright and other optical solitons to the decoupled nonlinear Schrodinger equation arising in dual-core optical fibers. Opt. Quantum Electron. 50(4), 165 (2018)
Conti, C., Peccianti, M., Assanto, G.: Route to nonlocality and observation of accessible solitons. Phys. Rev. Lett. 91, 073901 (2003)
d’Alessandro, A., Asquini, R.: Light propagation in confined nematic liquid crystals and device applications. Appl. Sci. 11, 8713 (2021). https://doi.org/10.3390/app11188713
Duran, S., Karabulut, B.: Nematicons in liquid crystals with Kerr law by sub-equation method. Alex. Eng. J. 61(2), 1695–1700 (2022). https://doi.org/10.1016/j.aej.2021.06.077
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(01), 1750005 (2017)
He, J.-H., Qie, N., He, C.-H.: Solitary waves travelling along an unsmooth boundary. Results Phys. 24, 104104 (2021a). https://doi.org/10.1016/j.rinp.2021.104104
He, J.-H., Hou, W.-F., He, C.-H., Saeed, T., Hayat, T.: Variational approach to fractal solitary waves. Fractals 29(07), 2150199 (2021b)
Ilhan, O.A., Manafian, J., Alizadeh, A., et al.: New exact solutions for nematicons in liquid crystals by the-expansion method arising in fluid mechanics. Eur. Phys. J. Plus 135, 313 (2020)
Inc, M., Az-Zo’bi, E.A., Jhangeer, A., Rezazadeh, H., Ali, M.N., Kaabar, M.K.A.: New soliton solutions for the higher-dimensional non-local Ito equation. Nonlinear Eng. 10(1), 374–384 (2021). https://doi.org/10.1515/nleng-2021-0029
Ismael, H.F., Bulut, H., Baskonus, H.M.: W-shaped surfaces to the nematic liquid crystals with three nonlinearity laws. Soft Comput. 25, 4513–4524 (2021). https://doi.org/10.1007/s00500-020-05459-6
Kavitha, L., Venkatesh, M., Gopi, D.: Shape changing nonlocal molecular deformations in a nematic liquid crystal system. J. Assoc. Arab Univ. Basic Appl. Sci. 18, 29–45 (2015)
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)
Khoo, I.C.: Liquid Crystals, 2nd edn. Wiley, New York (2007)
Kudryashov, N.A.: Simplest equation method to look for exact solutions of nonlinear differential equations. Chaos Solitons Fractals 24(5), 1217–1231 (2005a). https://doi.org/10.1016/j.chaos.2004.09.109
Kudryashov, N.A.: Exact solitary waves of the Fisher equation. Phys. Lett. A 342(1–2), 99–106 (2005b). https://doi.org/10.1016/j.physleta.2005.05.025
Kumar, D., Seadawy, A.R., Chowdhury, R.: On new complex soliton structures of the nonlinear partial differential equations describing the pulse narrowing nonlinear transmission lines. Opt. Quantum Electron. 50(2), 108 (2018)
Kumar, D., Joardar, A.K., Hoque, A., et al.: Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method. Opt. Quantum Electron. 51, 212 (2019). https://doi.org/10.1007/s11082-019-1917-6
Marchant, T.R., Smyth, N.: Approximate techniques for dispersive shock waves in nonlinear media. J. Nonlinear Opt. Phys. Mater. 21(3), 1250035 (2012)
Peccianti, M., Assanto, G.: Nematicons. Phys. Rep. 516, 147–208 (2012)
Pu, S., Hou, C., Yuan, C.: Soliton switching in inhomogeneous nonlocal media. Optik 125(3), 1075–1078 (2014)
Raza, N., Afzal, U., Butt, A.R., et al.: Optical solitons in nematic liquid crystals with Kerr and parabolic law nonlinearities. Opt. Quantum Electron. 51, 107 (2019). https://doi.org/10.1007/s11082-019-1813-0
Sala, F.A., Karpierz, M.A., Assanto, G.: Spatial routing with light-induced waveguides in uniaxial nematic liquid crystals. J. Nonlinear Opt. Phys. Mater. 23(4), 14500347 (2014)
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(11), 4667–4673 (2015)
Simoni, F.: Nonlinear Optical Properties of Liquid Crystals. World Scientific Publishing, London (1997)
Wang, M., Li, X., Zhang, J.: The \(\left( {G}^{\prime }/G\right)\)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372(4), 417–423 (2008). https://doi.org/10.1016/j.physleta.2007.07.051
Zayed, E.M.E., El-Ganaini, S.: Short comment on \(Tan(\varPhi /2)\)-expansion method proposed by Manafian and Lakestani. Optik 207, 163794 (2020). https://doi.org/10.1016/j.ijleo.2019.163794
Funding
Not applicable.
Author information
Authors and Affiliations
Contributions
ZA, EA and AOA conceived of the presented idea. They also developed the theory and performed the computations. MŞ and LA verified the analytical methods and plotted the figures. All authors provided critical feedback and helped shape the research and analysis of the manuscript. All authors reviewed and accepted the final version of the manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no competing interests.
Ethical approval
All authors agreed to participate and have consent to publish the manuscript.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Altawallbeh, Z., Az-Zo’bi, E., Alleddawi, A.O. et al. Novel liquid crystals model and its nematicons. Opt Quant Electron 54, 861 (2022). https://doi.org/10.1007/s11082-022-04279-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-022-04279-2