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New private types for the cubic-quartic optical solitons in birefringent fibers in its four forms of nonlinear refractive index

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Abstract

From the point of view of the extended simple equation method, multiple new private distinct types for the cubic-quartic optical soliton birefringent fibers with four forms nonlinear refractive index have been extracted. The suggested model has vital effective effect in all modern telecommunications process. The suggested method which has invited for this purpose examined previously for many other nonlinear problems arising in various branches of science and continuously gives good results. We will implement this method to extracting multiple new private types for the cubic-quartic soliton with its four different forms of the NLSE which are, the cubic-quartic in polarization-preserving fibers with the kerr-low nonlinearity, quadratic-cubic law nonlinearity, parabolic law nonlinearity and non-local law nonlinearity. Actual comparison between our achieved results and that realized previously by other authors has been established.

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References

  • Aksoy, E., Bekir, A., Cevikel, A.C.: Study on fractional differential equations with modified Riemann-Liouville derivative via Kudryashov method. Int. J. Nonlinear Sci. Numer. Simul. 20(5), 511 (2019)

    Article  MathSciNet  Google Scholar 

  • Amos, B.: Birefringence for factors I: what is birefringence? J. UK Facet Cut. Guild (2005)

  • Asma, M., Othman, W.A.M., Wong, B.R., Biswas, A.: Optical soliton perturbation with quadratic-cubic nonlinearity by Adomian decomposition method. Optik 164, 632–641 (2018)

    Article  ADS  Google Scholar 

  • Bansal, A., Biswas, A., Zhou, Q., Babatin, M.M.: Lie symmetry analysis for cubic-quartic nonlinear Schrödinger’s equation. Optik 169, 12–15 (2018)

    Article  ADS  Google Scholar 

  • Bartholin, E.: Experimenta crystalli islandici disdiaclastici quibus mira & infolita refractio detegitur [Experiments on birefringent Icelandic crystal through which is detected a remarkable and unique refraction] (Copenhagen, Denmark: Daniel Paulli, 1669).

  • Bekir, A., Zahran, E.H.M.: Bright and dark soliton solutions for the complex Kundu-Eckhaus equation. Optik. 223, 165233 (2020)

    Article  ADS  Google Scholar 

  • Bekir, A., Zahran, E.H.M.: New visions of the soliton solutions to the modified nonlinear Schrodinger equation. Optik-International Journal for Light and Electron Optics 232, 166539 (2021)

    Article  Google Scholar 

  • Bekir, A., Zahran, E.: Three distinct and impressive visions for the soliton solutions to the higher-order nonlinear Schrodinger equation. Optik 228, 166157 (2021)

    Article  ADS  Google Scholar 

  • Bekir, A., Zahran, E.H.M.: New multiple-different impressive perceptions for the solitary solution to the magneto-optic waveguides with anti-cubic nonlinearity; Optik – Int. J. Light Electron Opt. 240, 166939 (2021)

    Article  Google Scholar 

  • Bekir, A., Zahran, E.H.M.: New vision for the soliton solutions to the complex Hirota-dynamical model. Phys. Scr. 96, 055212 (2021)

    Article  ADS  Google Scholar 

  • Bekir, A., Güner, Ö., Ayhan, B., Cevikel, A.C.: Exact solutions for fractional differential-difference equations by (G’/G)-expansion method with modified Riemann-Liouville derivative. Adv. Appl. Math. Mech. 8(2), 293 (2016)

    Article  MathSciNet  Google Scholar 

  • Bekir, A., Güner, Ö., Cevikel, A.C.: The Exp-function method for some time-fractional differential equations. IEEE-CAA J. Autom. Sinica 4, 315 (2017)

    Article  MathSciNet  Google Scholar 

  • Bekir, A., Cevikel, A.C., Guner, O., San, S.: Bright and Dark Soliton Solutions of the (2 + 1)-dimensional evolution equations, Math. Model. Anal., Vol. 19 (2014)

  • Biswas, A., Arshed, S.: Application of semi-inverse variational principle to cubic-quartic optical solitons with Kerr and power law nonlinearity. Optik 172, 847–850 (2018)

    Article  ADS  Google Scholar 

  • Biswas, A., Ullah, M.Z., Asma, M., Zhou, Q., Moshokoa, S.P., Belic, B.: Optical solitons with quadratic-cubic nonlinearity by semi-inverse variational principle. Optik 139, 16–19 (2017a)

    Article  ADS  Google Scholar 

  • Biswas, A., Triki, H., Zhou, Q., Moshokoa, S.P., Ullah, M.Z., Belic, M.: Cubic-quartic optical solitons in Kerr and power law media. Optik 144, 357–362 (2017b)

    Article  ADS  Google Scholar 

  • Biswas, A., Kara, A.H., Ullah, M.Z., Zhou, Q., Triki, H., Belic, M.: Conservation laws for cubic-quartic optical solitons in Kerr and power law media. Optiki 145, 650–654 (2017c)

    Article  ADS  Google Scholar 

  • Biswas, A., Ullah, M.Z., Zhou, Q., Moshokoa, S.P., Triki, H., Belic, M.: Resonant optical solitons with quadratic-cubic nonlinearity by semi-inverse variational principle. Optik 145, 18–21 (2017d)

    Article  ADS  Google Scholar 

  • Cevikel, A.C.: New exact solutions of the space-time fractional KDV burgers and nonlinear fractional foam-drainage equation. Thermal Sci. 22(00), 267–267 (2018)

    Google Scholar 

  • Cevikel, A.C., Aksoy, E.: Soliton solutions of nonlinear fractional differential equations with their applications in mathematical physics. Revista Mexicana de F ́ısica 67(3), 422–428 (2021)

    Google Scholar 

  • Cevikel, A.C., Bekir, A.: New Solitons and Periodic Solutions for (2+1)-dimensional Davey-Stewartson Equations. Chin. J. Phys. 51, 11 (2013)

    MathSciNet  MATH  Google Scholar 

  • Cevikel, A., Bekir, A., San, S., Gucen, M.B.: Construction of periodic and solitary wave solutions for the complex nonlinear evolution equations. Franklin Inst. Eng. Appl. Math. 2, 694 (2014)

    Article  MathSciNet  Google Scholar 

  • Das, A., Biswas, A., Ekici, M., Khan, S., Zhou, Q., Moshokoa, S.P.: Suppressing internet bottleneck with fractional temporal evolution of cubic-quartic optical solitons. Optik 182, 303–307 (2019)

    Article  ADS  Google Scholar 

  • Gonzalez-Gaxiola, O., Biswas, A., Mallawi, F., Belic, M.: Cubic-quartic bright optical solitons by improved Adomian decomposition method. J. Adv. Res. 21, 161–167 (2020)

    Article  Google Scholar 

  • Güner, Ö., Bekir, A., Cevikel, A.C.: Dark soliton and periodic wave solutions of nonlinear evolution equations. Adv. Diff. Equ. 2013, 68 (2013)

    Article  MathSciNet  Google Scholar 

  • Hosseini, K., Sadri, K., Mirzazadeh, M., Chu, Y.M., Ahmadian, A., Pansera, B.A., Salahshour, S.: A high-order nonlinear Schrödinger equation with the weak non-local nonlinearity and its optical solitons. Results Phys. 23, 104035 (2021)

    Article  Google Scholar 

  • Hosseini, K., Salahshour, S., Mirzazadeh, M., Ahmadian, A., Baleanu, D., Khoshrang, A.: The (2 + 1)-dimensional Heisenberg ferromagnetic spin chain equation: its solitons and Jacobi elliptic function solutions. Eur. Phys. J. Plus 136, 206 (2021b)

    Article  Google Scholar 

  • Hosseini, K., Matinfar, M., Mirzazadeh, M.: Soliton solutions of high-order nonlinear Schrödinger equations with different laws of nonlinearities. Regular Chaotic Dyn. 26, 105–112 (2021c)

    Article  ADS  MathSciNet  Google Scholar 

  • Kohl, R.W., Biswas, A., Ekici, M., Zhou, Q., Moshokoa, S.P., Belic, M.R.: Cubic-quartic optical soliton perturbation by semi-inverse variational principle. Optik 185, 45–49 (2019)

    Article  ADS  Google Scholar 

  • Kudryashov, N.A.: Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations. Appl. Math. Comput. 371, 124972 (2020)

    MathSciNet  MATH  Google Scholar 

  • Lu, D., Seadawy, A., Arshad, M.: Applications of extended simple equation method on unstable nonlinear Schrödinger equations. Optik 140, 136–144 (2017)

    Article  ADS  Google Scholar 

  • Neves, N.M.: The use of birefringence for predicting the stiffness of injection molded polycarbonate discs. Polym. Eng. Sci. 38(10), 1770–1777 (1998)

    Article  Google Scholar 

  • Shehata, M.S.M., Rezazadeh, H., Jawad, A.J.M., Zahran, E.H.M., Bekir, A.: Optical solitons to a perturbed Gerdjikov-Ivanov equation using two different techniques. Revista Mexicana de F´ısica 67, 050704 (2020)

    Google Scholar 

  • Wazwaz, A.M., Xu, G.Q.: Bright, dark, and Gaussons optical solutions for fourth order Schrodinger equation with cubic-quantic and logarithmic nonlinearities. Optik. 202, 163564 (2020)

    Article  ADS  Google Scholar 

  • Yildirim, Y., Biswas, A., Guggilla, P., Mallawi, F., Belic, M.R.: Cubic-quartic optical solitons in birefringent fibers with four forms of nonlinear refractive index. Optik 203, 163885 (2020)

    Article  ADS  Google Scholar 

  • Yildirim, Y., Biswas, A., Jawad, A.J.M., Ekici, M., Zhou, Q., Khan, S., Alzahrani, A.K., Belic, M.R.: Cubic-quartic optical solitons in birefringent fibers with four forms of nonlinear refractive index by exp-function expansion. Results Phys. 16, 102913 (2020)

    Article  Google Scholar 

  • Zhao, Y.M., He, Y.H., Yao Long, Y.: The simplest equation method and its application for solving the nonlinear NLSE, KGZ, GDS, DS, and GZ equations. J. Appl. Math. 2013, 960798 (2013)

    MathSciNet  MATH  Google Scholar 

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Zahran, E.H.M., Bekir, A. New private types for the cubic-quartic optical solitons in birefringent fibers in its four forms of nonlinear refractive index. Opt Quant Electron 53, 680 (2021). https://doi.org/10.1007/s11082-021-03330-y

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