Abstract
The enterprising of nematicons has procured considerable recognition during the last few years due to its utilization in crystal technology. This research work contains some new exact traveling waves solutions in nematic liquid crystals. The modified simple equation method is employed to extract new traveling wave solutions. Two types of nonlinear mediums are investigated in this paper. New singular, periodic-singular and spatial solitons in liquid crystal are obtained by using analytical approach. The constraints fall out as the byproduct that guarantee their existence. The solutions are also highlighted graphically. This paper is leading to explore some unaccustomed results into this area of research.
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References
Abdullah, M., Butt, A.R., Raza, N., Haque, E.U.: Semi-analytical technique for the solution of fractional Maxwell fluid. Can. J. Phys. 94, 472–478 (2017)
Abdullah, M., Butt, A.R., Raza, N., Alshomrani, A.S., Alzahrani, A.K.: Analysis of blood flow with nanoparticles induced by uniform magnetic field through a circular cylinder with fractional Caputo derivatives. J. Magn. Magn. Mater. 446, 28–36 (2018)
Arnous, A.H., Mirzazadeh, M., Zhou, Q., Mahmood, M.F., Biswas, A., Belic, M.: Optical solitons with resonant nonlinear Schrodinger’s equation using G’/G-expansion scheme. Optoelectron. Adv. Mater. Rapid Commun. 9, 1214–1220 (2013)
Arnous, A.H., Mirzazadeh, M., Moshokoa, S., Medhekar, S., Zhou, Q., Mahmood, M.F., Biswas, A., Belic, M.: Solitons in optical metamaterials with trial solution approach and Backlund transform of Riccati equation. J. Comput. Theor. Nanosci. 12, 5940–5948 (2015)
Arnous, A.H., Ullah, M.Z., Moshokoa, S.P., Zhou, Q., Triki, H., Mirzazadeh, M., Biswas, A.: Optical solitons in birefringent fibres with modified simple equation method. Optik 130, 996–1003 (2017)
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)
Assanto, G., Karpierz, M.: Nematicons: self-localized beams in nematic liquid crystals. Liq. Cryst. 36, 1161–1172 (2009)
Crutcher, S.H., Osei, A.: The modulated spatial Gausson solution to Biswas–Milovic with log law nonlinearity. Optik 124, 4678–4681 (2013)
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 (2017)
El-Borai, M.M., El-Owaidy, H.M., Ahmed, H.M., Arnous, A.H., Moshokoa, S., Biswas, A., Belic, M.: Dark and singular optical solitons with spatio-temporal dispersion using modified simple equation method. Optik 130, 324–331 (2017)
Ferdi, Y.: Some applications of fractional order calculus to design digital filters for biomedical signal processing. J. Mech. Med. Biol. 12, 1240008 (2012)
Garca-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 (2006)
Kavitha, L., Venkatesh, M., Dhamayanthi, S., Gopi, D.: Nonlinear refractive index induced collision and propagation of nematicons. J. Mol. Liq. 197, 142–151 (2014)
Khoo, I.C., Wu, N.T.: Optics and Nonlinear Optics of Liquid Crystals. World Scientific Publishing, Singapore (1993)
Matusu, R.: Application of fractional order calculus to control theory. Int. J. Math. Models Methods Appl. Sci. 5, 1162–1169 (2011)
Mirzazadeh, M., Eslami, M.: Exact solutions for nonlinear variants of Kadomtsev–Petviashvili (n, n) equation using functional variable method. Pramana J. Phys. 81, 911–924 (2013)
Mirzazadeh, M., Arnous, A.H., Mahmood, M.F., Zerrad, E., Biswas, A.: Soliton solutions to the resonant nonlinear Schrodinger’s equation with time-dependant coefficients by trial solution approach. Nonlinear Dyn. 81, 277–282 (2015)
Qurashi, M.M.A., Ates, E., Inc, M.: Optical solitons in multiple-core couplers with nearest neighbours linear coupling. Optik 142, 343–353 (2017)
Raza, N., Javid, A.: Optical dark and singular solitons to the Biswas–Milovic equation in nonlinear optics with spatio-temporal dispersion. Optik 158, 1049–1057 (2018)
Raza, N., Murtaza, I.G., Sial, S., Younis, M.: On solitons: the biomolecular nonlinear transmission line models with constant and time variable coefficients. Waves Random Complex Med. 28, 553–569 (2017). https://doi.org/10.1080/17455030.2017.1368734
Raza, N., Abdullah, M., Butt, A.R.: Analytical soliton solutions of Biswas–Milovic equation in Kerr and non-Kerr law media. Optik 157, 993–1002 (2018a). https://doi.org/10.1016/j.ijleo.2017.11.043
Raza, N., Sial, S., Kaplan, M.: Exact periodic and explicit solutions of higher dimensional equations with fractional temporal evolution. Optik 156, 628–634 (2018b). https://doi.org/10.1016/j.ijleo.2017.11.107
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)
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, 1450045 (2014)
Simoni, F.: Nonlinear Optical Properties of Liquid Crystals. World Scientific Publishing, London (1997)
Tabiryan, N.V., Sukhov, A.V., Zel’dovich, B.Y.: Orientational optical nonlinearity of liquid crystals. Mol. Cryst. Liq. Cryst. 136, 1–139 (1986)
Wang, Q., Tong, D.: The flow analysis of viscoelastic fluid with fractional order derivative in horizontal well. Transp. Porous Med. 81, 295–303 (2010)
Wazwaz, A.M.: Gaussian solitary wave solutions for nonlinear evolution equations with logarithmic nonlinearities. Nonlinear Dyn. 83, 591–596 (2016a)
Wazwaz, A.M.: Multiple soliton solutions and multiple complex soliton solutions for two distinct Boussinesq equations. Nonlinear Dyn. 85, 731–737 (2016b)
Wazwaz, A.M., El-Tantawy, S.A.: A new (3 + 1)-dimensional generalized Kadomtsev Petviashvili equation. Nonlinear Dyn. 84, 1107–1112 (2016)
Xu, Y., Zhou, Q., Bhrawy, A.H., Khan, K.R., Mahmood, M.F., Biswas, A., Belic, M.: Bright soliton in optical metamaterials by traveling wave hypothesis. Optoelectron. Adv. Mater. Rapid Commun. 9, 384–387 (2015)
Younis, M., Ali, S., Mahmood, S.A.: Solitons for compound KdV–Burgers equation with variable coefficients and power law nonlinearity. Nonlinear Dyn. 81, 1191–1196 (2015)
Zayed, E.M.E., Arnous, A.H.: Exact solutions of the nonlinear ZK-MEW and the potential YTSF equations using the modified simple equation method. AIP Conf. Proc. 1479, 2044–2048 (2012)
Zhou, Q., Liu, S.: Dark optical solitons in quadratic nonlinear media with spatio-temporal dispersion. Nonlinear Dyn. 81, 733–738 (2015)
Zhou, Q., Zhu, Q., Yu, H., Liu, Y., Wei, C., Yao, P., Bhrawy, A.H., Biswas, A.: Bright, dark and singular optical solitons in a cascaded system. Laser Phys. 25, 25–40 (2015)
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Javid, A., Raza, N., Zhou, Q. et al. New exact spatial and periodic-singular soliton solutions in nematic liquid crystal. Opt Quant Electron 51, 147 (2019). https://doi.org/10.1007/s11082-019-1861-5
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DOI: https://doi.org/10.1007/s11082-019-1861-5