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Applied Physics B

, 125:104 | Cite as

New optical solutions of complex Ginzburg–Landau equation arising in semiconductor lasers

  • Orkun Tasbozan
  • Ali KurtEmail author
  • Ali Tozar
Article
  • 99 Downloads

Abstract

Nonlinear optics draws much attention by physicists and mathematicians due to its challenging mathematical structure. The study of non-hamiltonian and dissipative systems is one of the most complicated and challenging issues of nonlinear optics. Recent studies showed that there is a close relationship between superconductivity, Bose–Einstein condensation, and semiconductor lasers. Therefore, the cubic complex Ginzburg–Landau (CGLE) equation is thought to be a useful tool in investigating nonlinear optical events. On the other hand, the CGLE is a very general type of equation that governing a vast variety of bifurcations and nonlinear wave phenomena in spatiotemporally extended systems. In this article, we acquire the new wave solution of time fractional CGLE with the aid of Jacobi elliptic expansion method.

Mathematics Subject Classification

35R11 34A08 35A20 26A33 

Notes

References

  1. 1.
    H. Rezazadeh, M.S. Osman, M. Eslami, M. Mirzazadeh, Q. Zhou, S.A. Badri, A. Korkmaz, Hyperbolic rational solutions to a variety of conformable fractional Boussinesq-Like equations. Nonlinear Eng. 8(1), 224–230 (2019)ADSCrossRefGoogle Scholar
  2. 2.
    K.U. Tariq, M. Younis, H. Rezazadeh, S.T.R. Rizvi, M.S. Osman, Optical solitons with quadratic-cubic nonlinearity and fractional temporal evolution. Modern Phys. Lett. B 32(26), 1850317 (2018)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    M.S. Osman, Multiwave solutions of time-fractional (2+1)-dimensional Nizhnik-Novikov-Veselov equations. Pramana 88(4), 67 (2017)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    H.I. Abdel-Gawad, M.S. Osman, On the variational approach for analyzing the stability of solutions of evolution equations. Kyungpook Math. J. 53(4), 661–680 (2013)MathSciNetCrossRefGoogle Scholar
  5. 5.
    M.S. Osman, One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient Sawada–Kotera equation. Nonlinear Dyn. 96, 1491–1496 (2019)CrossRefGoogle Scholar
  6. 6.
    M.S. Osman, J.A.T. Machado, New nonautonomous combined multi-wave solutions for (2+1)-dimensional variable coefficients KdV equation. Nonlinear Dyn. 93, 733–740 (2018)CrossRefGoogle Scholar
  7. 7.
    M.S. Osman, J.A.T. Machado, The dynamical behavior of mixed-type soliton solutions described by (2+ 1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients. J. Electromagn. Waves Appl. 32(11), 1457–1464 (2018)CrossRefGoogle Scholar
  8. 8.
    M.S. Osman, H.I. Abdel-Gawad, M.A. El Mahdy, Two- layer-atmospheric blocking in a medium with high nonlinearity and lateral dispersion. Results Phys. 8, 1054–1060 (2018)ADSCrossRefGoogle Scholar
  9. 9.
    M.S. Osman, B. Ghanbari, New optical solitary wave solutions of Fokas-Lenells equation in presence of perturbation terms by a novel approach. Optik 175, 328–333 (2018)ADSCrossRefGoogle Scholar
  10. 10.
    M.S. Osman, B. Ghanbari, J.A.T. Machado, New complex waves in nonlinear optics based on the complex Ginzburg-Landau equation with Kerr law nonlinearity. Eur. Phys. J. Plus 134(1), 20 (2019)CrossRefGoogle Scholar
  11. 11.
    H.I. Abdel-Gawad, M. Osman, On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients. J. Adv. Res. 6(4), 593–599 (2015)CrossRefGoogle Scholar
  12. 12.
    I.H. Abdel-Gawad, S.N. Elazab, M. Osman, Exact solutions of space dependent Korteweg-de Vries equation by the extended unified method. J. Phys. Soc. Jpn. 82(4), 044004 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    Q. Zhou, D. Kumar, M. Mirzazadeh, M. Eslami, H. Rezazadeh, Optical soliton in nonlocal nonlinear medium with cubic-quintic nonlinearities and spatio-temporal dispersion. Acta Phys. Polonica A 134(6), 1204–1210 (2018)CrossRefGoogle Scholar
  14. 14.
    M.S. Osman, H. Rezazadeh, M. Eslami, A. Neirameh, M. Mirzazadeh, Analytical study of solitons to benjamin-bona-mahony-peregrine equation with power law nonlinearity by using three methods. Univ. Politehnica Buchrest Sci. Bull. Ser. A Appl. Math. Phys. 80(4), 267–278 (2018)MathSciNetzbMATHGoogle Scholar
  15. 15.
    A. Biswas, H. Rezazadeh, M. Mirzazadeh, M. Eslami, M. Ekici, Q. Zhou, S.P. Moshokoa, M. Belic, Optical soliton perturbation with Fokas-Lenells equation using three exotic and efficient integration schemes. Optik 165, 288–294 (2018)ADSCrossRefGoogle Scholar
  16. 16.
    A. Biswas, M.O. Al-Amr, H. Rezazadeh, M. Mirzazadeh, M. Eslami, Q. Zhou, S.P. Moshokoa, M. Belic, Resonant optical solitons with dual-power law nonlinearity and fractional temporal evolution. Optik 165, 233–239 (2018)ADSCrossRefGoogle Scholar
  17. 17.
    N. Raza, M.R. Aslam, H. Rezazadeh, Analytical study of resonant optical solitons with variable coefficients in Kerr and non-Kerr law media. Opt. Quantum Electron. 51(2), 59 (2019)CrossRefGoogle Scholar
  18. 18.
    H. Rezazadeh, A. Korkmaz, M. Eslami, S.M. Mirhosseini-Alizamini, A large family of optical solutions to Kundu-Eckhaus model by a new auxiliary equation method. Opt. Quantum Electron. 51(3), 84 (2019)CrossRefGoogle Scholar
  19. 19.
    A. Biswas, H. Rezazadeh, M. Mirzazadeh, M. Eslami, Q. Zhou, S.P. Moshokoa, M. Belic, Optical solitons having weak non-local nonlinearity by two integration schemes. Optik 164, 380–384 (2018)ADSCrossRefGoogle Scholar
  20. 20.
    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)ADSCrossRefGoogle Scholar
  21. 21.
    H. Yépez-Martínez, H. Rezazadeh, A. Souleymanou, S.P.T. Mukam, M. Eslami, V.K. Kuetche, A. Bekir, The extended modified method applied to optical solitons solutions in birefringent fibers with weak nonlocal nonlinearity and four wave mixing. Chin. J. Phys. 58, 137–150 (2019)CrossRefGoogle Scholar
  22. 22.
    H. Rezazadeh, S.M. Mirhosseini-Alizamini, M. Eslami, M. Rezazadeh, M. Mirzazadeh, S. Abbagari, New optical solitons of nonlinear conformable fractional Schrödinger-Hirota equation. Optik 172, 545–553 (2018)ADSCrossRefGoogle Scholar
  23. 23.
    H. Rezazadeh, New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity. Optik 167, 218–227 (2018)ADSCrossRefGoogle Scholar
  24. 24.
    H. Rezazadeh, H. Tariq, M. Eslami, M. Mirzazadeh, Q. Zhou, New exact solutions of nonlinear conformable time-fractional Phi-4 equation. Chin. J. Phys. 56(6), 2805–2816 (2018)CrossRefGoogle Scholar
  25. 25.
    S. Echeverri-Arteaga, H. Vinck-Posada, E.A. Gomez, A study on the role of the initial conditions and the nonlinear dissipation in the non-Hermitian effective Hamiltonian approach. Optik 174, 114–120 (2018)ADSCrossRefGoogle Scholar
  26. 26.
    K. Kumara, T.C.S. Shetty, S.R. Maidur, P.S. Patil, S.M. Dharmaprakash, Continuous wave laser induced nonlinear optical response of nitrogen doped graphene oxide. Optik 178, 384–393 (2019)ADSCrossRefGoogle Scholar
  27. 27.
    W.T. Yu, M. Ekici, M. Mirzazadeh, Q. Zhou, W. Liu, Periodic oscillations of dark solitons in nonlinear optics. Optik 165, 341–344 (2018)ADSCrossRefGoogle Scholar
  28. 28.
    A. Berti, V. Berti, A thermodynamically consistent Ginzburg-Landau model for superfluid transition in liquid helium. Zeitschrift Fur Angewandte Mathematik Und Physik 64(4), 1387–1397 (2013)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    E. Kengne, A. Lakhssassi, R. Vaillancourt, W.M. Liu, Exact solutions for generalized variable-coefficients Ginzburg-Landau equation: application to Bose-Einstein condensates with multi-body interatomic interactions. J. Math. Phys. 53(12), 28 (2012)MathSciNetCrossRefGoogle Scholar
  30. 30.
    R.J. Rivers, Zurek-Kibble causality bounds in time-dependent Ginzburg-Landau theory and quantum field theory. J. Low Temp. Phys. 124(1–2), 41–83 (2001)ADSCrossRefGoogle Scholar
  31. 31.
    M.S. Osman, On complex wave solutions governed by the 2D Ginzburg-Landau equation with variable coefficients. Optik 156, 169–174 (2018)ADSCrossRefGoogle Scholar
  32. 32.
    J. Park, P. Strzelecki, Bifurcation to traveling waves in the cubic-quintic complex Ginzburg-Landau equation. Anal. Appl. 13(4), 395–411 (2015)MathSciNetCrossRefGoogle Scholar
  33. 33.
    K. Krischer, The complex Ginzburg-Landau equation: an introduction AU—García-Morales. Vladimir. Contemp. Phys. 53(2), 79–95 (2012)ADSCrossRefGoogle Scholar
  34. 34.
    A.M. Abourabia, R.A. Shahein, Modulational instability and exact solutions of nonlinear cubic complex Ginzburg-Landau equation of thermodynamically open and dissipative warm ion acoustic waves system. Eur. Phys. J. Plus 126(2), 28 (2011)CrossRefGoogle Scholar
  35. 35.
    T. Horikiri et al., High-energy side-peak emission of exciton-polariton condensates in high density regime. Sci. Rep. 6, 25655 (2016)ADSCrossRefGoogle Scholar
  36. 36.
    R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative. J. Comput. Appl. Math. 264, 65–70 (2014)MathSciNetCrossRefGoogle Scholar
  37. 37.
    T. Abdeljawad, On conformable fractional calulus. J. Comput. Appl. Math. 279, 57–66 (2015)MathSciNetCrossRefGoogle Scholar
  38. 38.
    S. Lai, X. Lv, M. Shuai, The Jakobi elliptic function solutions to a generalized Benjamin-Bona-Mahony equation. Math. Comput. Model. 49, 369–378 (2009)CrossRefGoogle Scholar
  39. 39.
    H.M. Li, New exact solutions of nonlinear Gross-Pitaevskii eqauation with weak bias magnetic and time-dependent laser fields. Chin. Phys. 14, 251–256 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsHatay Mustafa Kemal UniversityHatayTurkey
  2. 2.Department of MathematicsPamukkale UniversityDenizliTurkey
  3. 3.Department of PhysicsHatay Mustafa Kemal UniversityHatayTurkey

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