Optical Gaussons and dark solitons in directional couplers with spatiotemporal dispersion

  • Farida Tahir
  • Muhammad YounisEmail author
  • Hamood Ur Rehman


This paper study the dynamics of optical solitons for nonlinear directional couplers. This coupler system is considered with the group velocity dispersion and the cross-phase modulation of two components along with the spatiotemporal dispersion coefficients. The constraint conditions for the existence of optical Gaussons and dark solitons are listed under the log law and Kerr law nonlinearities, repectively. Additionally, a couple of other solutions known as singular periodic and combined dark-singular solitons, fall out as a by-product of this scheme. This scheme however fails to retrieve bright soliton solution.


Optical solitons Directional couplers Integrability 


  1. 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 bcklund transform of Riccati equation. J. Comput. Theor. Nanosci. 12, 5940–5948 (2015)CrossRefGoogle Scholar
  2. Arnous, A.H., Mirzazadeh, M., Zhou, Q., Moshokoa, S.P., Biswas, A., Belic, M.: Soliton solutions to resonant nonlinear schrodingers equation with time-dependent coefficients by modified simple equation method. Optik 127, 11450–11459 (2016)ADSCrossRefGoogle Scholar
  3. Biswas, A., Lott, D.A., Sutton, B., Khan, K.R., Mahommd, M.F.: Optical Gaussons in nonlinear directional couplers. J. Electromagn. Waves Appl. 27, 1976–1985 (2013)CrossRefGoogle Scholar
  4. Cheemaa, N., Mehmood, S.A., Rizvi, S.T.R., Younis, M.: Single and combined optical solitons with third order dispersion in Kerr media. Optik 127, 8203–8208 (2016)ADSCrossRefGoogle Scholar
  5. Islam, W., Younis, M., Rizvi, S.T.R.: Optical solitons with time fractional nonlinear Schrodinger equation and competing weakly nonlocal nonlinearity. Optik 130, 562–567 (2017)ADSCrossRefGoogle Scholar
  6. Liu, W.-J., Tian, B.: Symbolic computation on soliton solutions for variable-coefficient nonlinear Schrdinger equation in nonlinear optics. Opt. Quantum Electron. 43, 147–162 (2012)CrossRefGoogle Scholar
  7. Majid, F.: 1-soliton solution of the Biswas–Milovic equation with log law nonlinearity. Casp. J. Math. Sci. 3(1(2)), 88–93 (2012)Google Scholar
  8. Mirzazadeh, M., Biswas, A.: Optical solitons with spatio-temporal dispersion by first integral approach and functional variable method. Optik 125, 5467–5475 (2014)ADSCrossRefGoogle Scholar
  9. Mirzazadeh, M., Eslami, M., Zerrad, E., Mahommd, M.F., Biswas, A., Belic, M.: Optical solitons in nonlinear directional couplers by sine–cosine function method and Bernoulli’s equation approach. Nonlinear Dyn. 81, 1933–1949 (2015)MathSciNetCrossRefGoogle Scholar
  10. Rizvi, S.T.R., Ali, I., Ali, K., Younis, M.: Saturation of the nonlinear refractive index for optical solitons in two-core fibers. Optik 127, 5328–5333 (2016)ADSCrossRefGoogle Scholar
  11. Taghizadeh, N., Mirzazadeh, M., Paghaleh, A.S.: Exact solutions for the nonlinear Schrodinger equation with power law nonlinearity. Math. Sci. Lett. 1, 7–16 (2012)CrossRefGoogle Scholar
  12. Tian, S.-F.: The mixed coupled nonlinear Schrodinger equation on the half-line via the Fokas method. Proc. R. Soc. A. 472, 20160588 (2016)ADSMathSciNetCrossRefGoogle Scholar
  13. Tian, S.-F.: Initialboundary value problems for the general coupled nonlinear Schrodinger equation on the interval via the Fokas method. J. Differ. Equ. 262, 506–558 (2017)ADSCrossRefGoogle Scholar
  14. Younis, M., Rizvi, S.T.R.: Dispersive dark optical soliton in (2+1)-dimensions by G’/G-expansion with dual-power law nonlinearity. Optik 126, 5812–5814 (2015)ADSCrossRefGoogle Scholar
  15. Younis, M., Rizvi, S.T.R.: Optical soliton like-pulses in ring-cavity fiber lasers of carbon nanotubes. J. Nanoelectron. Optoelectron. 11, 276–279 (2016)CrossRefGoogle Scholar
  16. Younis, M., Cheemaa, N., Rizvi, S.T.R., Mahmood, M.F., Zhou, Q., Zerrad, E., Biswas, A., Belic, M.: Optical gaussons in dual-core nano-fibers. J. Comput. Theor. Nanosci. 12, 5745–5748 (2015)CrossRefGoogle Scholar
  17. Younis, M., Cheemaa, N., Rizvi, S.T.R., Mehmood, S.A.: On optical solitons: the chiral nonlinear Schrodinger equation with perturbation and Bohm potential. Opt. Quantum Electron. 48, 542–556 (2016)CrossRefGoogle Scholar
  18. Zhou, Q., Yao, D., Chen, F., Li, W.: Optical solitons in gas-filled, hollow-core photonic crystal fibers with inter-modal dispersion and self-steepening. J. Mod. Opt. 60(10), 854–859 (2013)ADSMathSciNetCrossRefGoogle Scholar
  19. Zhou, Q., Mirzazadeh, M., Ekici, M., Sonmezoglu, A.: Analytical study of solitons in non-Kerr nonlinear negative-index materials. Nonlinear Dyn. 86, 623–638 (2016)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • Farida Tahir
    • 1
  • Muhammad Younis
    • 2
    Email author
  • Hamood Ur Rehman
    • 3
  1. 1.Department of MathematicsNational College of Business Administration and EconomicsLahorePakistan
  2. 2.Centre of Undergraduate StudiesUniversity of the PunjabLahorePakistan
  3. 3.Department of MathematicsUniversity of the OkaraOkaraPakistan

Personalised recommendations