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New exact solutions for nematicons in liquid crystals by the \(\tan (\phi /2)\)-expansion method arising in fluid mechanics

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Abstract

In this research paper, we try to illustrate the structure of the novel exact soliton wave solutions of nematicons in liquid crystals with four law nonlinearity forms including the Kerr, power, parabolic and dual-power by utilizing the \(\tan (\phi /2)\)-expansion method. The aim of this research is not just to find the dark, bright, combined dark-bright, singular types, traveling and solitary solutions of nematicons in liquid crystals by investigating the aforementioned method, showing the differences between the obtained solutions and other solutions obtained by using different methods. Moreover, constraints guarantee the existence of the obtained solutions. Eventually, we believe that the enforced method is more powerful and efficient than other methods and the obtained solutions in this paper can help us to understand soliton molecules in liquid crystals. That will be extensively used to describe many interesting physical phenomena in the areas of gas, plasma, optics, acoustics, fluid dynamics, classical mechanics and so on.

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References

  1. M.R. Foroutan, J. Manafian, A. Ranjbaran, Optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity by analytical methods. Opt. Quantum Electron. 50(97), 1–19 (2018)

    Google Scholar 

  2. J. Manafian, Optical solitons in a power-law media with fourth order dispersion by three integration methods. Cogent Math. Stat. 5(1434924), 1–15 (2018)

    MathSciNet  MATH  Google Scholar 

  3. A.H. Arnous, M.Z.U. Seithuti, P. Moshokoa, Q. Zhou, H. Triki, M. Mirzazadeh, A. Biswas, Optical solitons in nonlinear directional couplers with trial function scheme. Nonlinear Dyn. 88, 1891–1915 (2017)

    MATH  Google Scholar 

  4. J. Manafian, M. Lakestani, Dispersive dark optical soliton with Tzitzéica type nonlinear evolution equations arising in nonlinear optics. Opt. Quantum Electron. 48, 1–32 (2016)

    Google Scholar 

  5. J. Manafian, Optical soliton solutions for Schrödinger type nonlinear evolution equations by the \(tan(\phi /2)\)-expansion method. Optik Int. J. Electron Opt. 127, 4222–4245 (2016)

    Google Scholar 

  6. J. Manafian, M. Lakestani, Optical soliton solutions for the Gerdjikov–Ivanov model via \(tan(\phi /2)\)-expansion method. Optik 127, 9603–9620 (2016)

    ADS  Google Scholar 

  7. J. Manafian, M. Lakestani, Optical solitons with Biswas–Milovic equation for Kerr law nonlinearity. Eur. Phys. J. Plus 130, 1–12 (2015)

    Google Scholar 

  8. J. Manafian, On the complex structures of the Biswas–Milovic equation for power, parabolic and dual parabolic law nonlinearities. Eur. Phys. J. Plus 130, 1–20 (2015)

    Google Scholar 

  9. A.R. Aly, J. Manafian, New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod. Results Phys. 8, 1158–1167 (2018)

    ADS  Google Scholar 

  10. M. Lakestani, J. Manafian, Analytical treatment of nonlinear conformable timefractional Boussinesq equations by three integration methods. Opt. Quantum Electron. 50(4), 1–31 (2018)

    Google Scholar 

  11. J. Manafian, M.F. Aghdaei, M. Khalilian, R.S. Jeddi, Application of the generalized G\(^{\prime }\)/G-expansion method for nonlinear PDEs to obtaining soliton wave solution. Optik 135, 395–406 (2017)

    ADS  Google Scholar 

  12. C.T. Sindi, J. Manafian, Wave solutions for variants of the KdV–Burger and the K(n, n)-Burger equations by the generalized G\(^{\prime }\)/G-expansion method. Math. Methods Appl. Sci. (2017). https://doi.org/10.1002/mma.4309

    Article  MathSciNet  MATH  Google Scholar 

  13. C.T. Sindi, J. Manafian, Soliton solutions of the quantum Zakharov–Kuznetsov equation which arises in quantum magneto-plasmas. Eur. Phys. J. Plus 132, 67 (2017). https://doi.org/10.1140/epjp/i2017-11354-7

    Article  Google Scholar 

  14. H. Bulut, T.A. Sulaiman, H.M. Baskonus, Dark, bright and other soliton solutions to the Heisenberg ferromagnetic spin chain equation. Superlattices Microstruct. (2017). https://doi.org/10.1016/j.spmi.2017.12.009

    Article  Google Scholar 

  15. H.M. Baskonus, T.A. Sulaiman, H. Bulut, T. Akturk, Investigations of dark, bright, combined dark–bright optical and other soliton solutions in the complex cubic nonlinear Schrödinger equation with \(\delta \)-potential. Superlattices Microstruct. (2018). https://doi.org/10.1016/j.spmi.2018.01.008

    Article  Google Scholar 

  16. H. Bulut, T.A. Sulaiman, H.M. Baskonus, On the solitary wave solutions to the longitudinal wave equation in MEE circular rod. Opt. Quantum Electron. 50(2), 87 (2018)

    Google Scholar 

  17. D. Kumar, J. Manafian, F. Hawlader, A. Ranjbaran, New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method. Optik 160, 159–167 (2018)

    ADS  Google Scholar 

  18. M.R. Foroutan, D. Kumar, J. Manafian, A. Hoque, New explicit soliton and other solutions for the conformable fractional Biswas–Milovic equation with Kerr and parabolic nonlinearity through an integration scheme. Optik 170, 190–202 (2018)

    ADS  Google Scholar 

  19. A.J.M. Jawad, M.J.A. AlShaeer, F.B. Majid, A. Biswas, Q. Zhou, M. Belic, Optical soliton perturbation with exotic non-Kerr law nonlinearities. Optik 158, 1370–1379 (2018)

    ADS  Google Scholar 

  20. A. Biswas, M. Ekici, A. Sonmezoglu, H. Triki, Q. Zhou, S.P. Moshokoa, M. Belic, Dispersive optical solitons with differential group delay by extended trial equation method. Optik 158, 790–798 (2018)

    ADS  Google Scholar 

  21. A. Biswas, M. Ekici, A. Sonmezoglu, F.B. Majid, H. Triki, Q. Zhou, S.P. Moshokoa, M. Belic, Optical soliton perturbation for Gerdjikov–Ivanov equation by extended trial equation method. Optik 158, 747–752 (2018)

    ADS  Google Scholar 

  22. A.H. Arnous, A.R. Seadawy, R.T. Alqahtani, A. Biswas, Optical solitons with complex Ginzburg–Landau equation by modified simple equation method. Optik 144, 475–480 (2017)

    ADS  Google Scholar 

  23. A. Biswas, Y. Yildirim, E. Yasar, H. Triki, A.S. Alshomrani, M.Z. Ullah, Q. Zhou, S.P. Moshokoa, M. Belic, Optical soliton perturbation with full nonlinearity by trial equation method. Optik 157, 1366–1375 (2018)

    ADS  Google Scholar 

  24. A. Biswas, Y. Yildirim, E. Yasar, Q. Zhou, S.P. Moshokoa, M. Belic, Optical solitons with differential group delay by trial equation method. Optik 160, 116–123 (2018)

    ADS  Google Scholar 

  25. A. Biswas, M. Ekici, A. Sonmezoglu, Q. Zhou, A.S. Alshomrani, S.P. Moshokoa, M. Belic, Optical network topology with DWDM technology for log law medium. Optik 160, 353–360 (2018)

    ADS  Google Scholar 

  26. A. Biswas, Q. Zhou, H. Triki, M.Z. Ullah, M. Asma, S.P. Moshokoa, M. Belic, Resonant optical solitons with parabolic and dual-power laws by semi-inverse variational principle. J. Mod. Opt. 65, 179–184 (2018)

    ADS  MathSciNet  Google Scholar 

  27. J. Manafian, Optical soliton solutions for Schrödinger type nonlinear evolution equations by the \(tan(\phi /2)\)-expansion method. Optik 127, 4222–4245 (2016)

    ADS  Google Scholar 

  28. Q. Zhou, Q. Zhu, Y. Liu, A. Biswas, A.H. Bhrawy, K.R. Khan, M.F. Mahmood, M. Belic, Solitons in optical metamaterials with parabolic law nonlinearity and spatio-temporal dispersion. J. Optoelectron. Adv. Mater. 16(11–12), 1221–1225 (2014)

    Google Scholar 

  29. M. Ekici, A. Sonmezoglu, Q. Zhou, S.P. Moshokoa, M.Z. Ullah, A.H. Arnous, A. Biswas, M. Belic, Analysis of optical solitons in nonlinear negative-indexed materials with anti-cubic nonlinearity. Opt. Quantum Electron. 50, 75 (2018)

    Google Scholar 

  30. M.R. Foroutan, J. Manafian, A. Ranjbaran, Solitons in optical metamaterials with anti-cubic law of nonlinearity by generalized G\(^{\prime }\)/G-expansion method. Optik 162, 86–94 (2018)

    ADS  Google Scholar 

  31. M.R. Foroutan, J. Manafian, I. Zamanpour, Soliton wave solutions in optical metamaterials with anti-cubic law of nonlinearity by ITEM. Optik 164, 371–379 (2018)

    ADS  Google Scholar 

  32. M. Ekici, M. Mirzazadeh, A. Sonmezoglu, M.Z. Ullah, Q. Zhou, S.P. Moshokoa, A. Biswas, M. Belic, Nematicons in liquid crystals by extended trial equation method. J. Nonlinear Opt. Phys. Mater. 26(1750005), 1–30 (2017)

    Google Scholar 

  33. A.H. Arnous, M.Z. Ullah, M. Asma, S.P. Moshokoa, M. Mirzazadeh, A. Biswas, M. Belic, Nematicons in liquid crystals by modified simple equation method. Nonlinear Dyn. 88, 2863–2872 (2017)

    MathSciNet  Google Scholar 

  34. A. Alberucci, G. Assanto, Dissipative self-confined optical beams in doped nematic liquid crystals. J. Nonlinear Opt. Phys. Mater. 16(3), 295–305 (2007)

    ADS  Google Scholar 

  35. G. Assanto, M. Peccianti, C. Conti, Spatial optical solitons in bulk nematic liquid crystals. Acta Phys. Pol. A 103(2–3), 161–167 (2003)

    Google Scholar 

  36. G. Assanto, M. Peccianti, K.R. Brzdakiewicz, A.D. Luca, C. Umeton, Nonlinear wave propagation and spatial solitons in nematic liquid crystals. J. Nonlinear Opt. Phys. Mater. 12(2), 123–134 (2003)

    ADS  Google Scholar 

  37. G. Assanto, C. Umeton, M. Peccianti, A. Alberucci, Nematicons and their angular steering. J. Nonlinear Opt. Phys. Mater. 15(1), 33–42 (2006)

    ADS  Google Scholar 

  38. G. Assanto, M. Peccianti, Routing light at will. J. Nonlinear Opt. Phys. Mater. 16(1), 37–47 (2007)

    ADS  Google Scholar 

  39. M.S. Chychlowski, S. Ertman, M.M. Tefelska, T.R. Wolinski, E. Nowinowski-Kruszelnicki, O. Yaroshchuk, Photo-induced orientation of nematic liquid crystals in microcapillaries. Acta Phys. Pol. 118(6), 1100–1103 (2010)

    Google Scholar 

  40. M.A. Karpierz, Nonlinear properties of waveguides with twisted nematic liquid crystal. Acta Phys. Pol. A 99(1), 161–173 (2001)

    Google Scholar 

  41. L. Kavitha, M. Venkatesh, D. Gopi, Shape changing nonlocal molecular deformations in a nematic liquid crystal system. J. Assoc. Arab Univ. Basic Appl. Sci. 18, 29–45 (2015)

    Google Scholar 

  42. L. Pezzi, A. Veltri, A.D. Luca, C. Umeton, Model for molecular director configuration in a liquid crystal cell with multiple interfaces. J. Nonlinear Opt. Phys. Mater. 16(2), 199–206 (2007)

    ADS  Google Scholar 

  43. S. Pu, C. Hou, C. Yuan, Soliton switching in inhomogeneous nonlocal media. Optik 125(3), 1075–1078 (2014)

    ADS  Google Scholar 

  44. A.I. Strinic, M.R. Belic, Beam propagation in nematic liquid crystals. Acta Phys. Pol. A 112(5), 877–883 (2007)

    ADS  Google Scholar 

  45. A.I. Strinic, M. Petrovic, M.R. Belic, Hyper-solitons in nematic liquid crystals. Acta Phys. Pol. A 116(4), 510–512 (2009)

    ADS  Google Scholar 

  46. Z. Xu, N.F. Smyth, A.A. Minzoni, Y.S. Kivshar, Vector vortex solitons in nematic liquid crystals. Opt. Lett. 34(9), 1414–1416 (2009)

    ADS  Google Scholar 

  47. M. Savescu, S. Johnson, P. Sanchez, Q. Zhou, M.F. Mahmood, E. Zerrad, A. Biswas, M. Belic, Nematicons in liquid crystals. J. Comput. Theor. Nanosci. 12(11), 4667–4673 (2015)

    Google Scholar 

  48. H. Rezazadeh, A. Korkmaz, M.M.A. Khater, M. Eslami, D. Lu, R.A.M. Attia, New exact traveling wave solutions of biological population model via the extended rational sinh-cosh method and the modified Khater method. Mod. Phys. Lett. B 33(28), 1950338 (2019)

    ADS  MathSciNet  Google Scholar 

  49. A. Souleymanou, K.K. Ali, H. Rezazadeh, M. Eslami, M. Mirzazadeh, A. Korkmaz, The propagation of waves in thin-film ferroelectric materials. Pramana 93, 27 (2019)

    ADS  Google Scholar 

  50. H. Rezazadeh, S.M. Mirhosseini-Alizamini, M. Eslami, M.R. Rezazadeh, M. Mirzazadehe, S. Abbagari, New optical solitons of nonlinear conformable fractional Schrödinger–Hirota equation. Optik 172, 545–553 (2018)

    ADS  Google Scholar 

  51. H. Bulut, T.A. Sulaiman, H.M. Baskonus, H. Rezazadeh, M. Eslami, M. Mirzazadeh, Optical solitons and other solutions to the conformable space–time fractional Fokas–Lenells equation. Optik 172, 20–27 (2018)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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Acknowledgements

The authors would like to thank the respected reviewer for providing the given comments and valuable recommendations which improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Erciyes University, 38039, Melikgazi, Kayseri, Turkey

    Onur Alp Ilhan

  2. Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran

    Jalil Manafian

  3. Department of Mechanical Engineering, Urmia University of Technology, Urmia, Iran

    As’ad Alizadeh

  4. Department of Mechanical Engineering, College of Engineering, University of Zakho, Zakho, Iraq

    As’ad Alizadeh

  5. Department of Mathematics and Science Education, Faculty of Education, Harran University, Şanlıurfa, Turkey

    Haci Mehmet Baskonus

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  1. Onur Alp Ilhan
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  2. Jalil Manafian
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Correspondence to Onur Alp Ilhan.

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Ilhan, O.A., Manafian, J., Alizadeh, A. et al. New exact solutions for nematicons in liquid crystals by the \(\tan (\phi /2)\)-expansion method arising in fluid mechanics. Eur. Phys. J. Plus 135, 313 (2020). https://doi.org/10.1140/epjp/s13360-020-00296-w

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