Ukrainian Journal of Physical Optics 

Volume 22, Issue 4, 2021

Home page
 
 

Other articles 

in this issue
Cubic–quartic optical solitons having quadratic–cubic nonlinearity by sine–Gordon equation approach

1Yakup Yıldırım, 2,3,4,5Anjan Biswas, 6,7Anelia Dakova, 5Padmaja Guggilla, 5Salam Khan, 3Hashim M. Alshehri and 8Milivoj R. Belic

1Department of Mathematics, Faculty of Arts and Sciences, Near East   University, 99138 Nicosia, Cyprus
2Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Hwy, Moscow–115409, Russian Federation
3Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah–21589, Saudi Arabia
4Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa–0204, Pretoria, South Africa
5Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762–4900, USA
6Physics and Technology Faculty, University of Plovdiv ``Paisii Hilendarski", 24 Tsar Asen Street, 4000 Plovdiv, Bulgaria
7Institute of Electronics, Bulgarian Academy of Sciences, 72 Tzarigradcko Shossee, 1784 Sofia, Bulgaria
8Institute of Physics Belgrade, Pregrevica 118, 11080 Zemun, Serbia

Download this article

Abstract. This paper recovers cubic–quartic optical solitons with quadratic–cubic nonlinearity for the first time. Both polarization–preserving fibers as well as birefringent fibers are considered. The study is subsequently extended to include perturbation terms that are of Hamiltonian type. The adopted integration algorithm is the sine–Gordon equation method

Keywords: solitons, quadratic–cubic nonlinearity, birefringence, perturbation

UDC: 535.32
Ukr. J. Phys. Opt. 22 255-269
doi: 10.3116/16091833/22/4/255/2021
Received: 22.10.2021

Анотація. Вперше виявлено кубічно-квартичні оптичні солітони з квадратично-кубічної нелінійністю. Розглянуто як поляризаційні волокна, так і волокна з подвійним заломленням. Дослідження також розширено на випадок розгляду членів збурення гамільтонового типу. Алгоритмом інтегрування, прийнятим у цій роботі, є метод рівняння синус-Гордона.

REFERENCES
  1. Asma M, Othman W A M, Wong B R and Biswas A, 2017. Optical soliton perturbation with quadratic-cubic nonlinearity by semi-inverse variational principle. Proc. Rom. Acad. A. 18: 331−336.
  2. Asma M, Othman W A M, Wong B R and Biswas A, 2017. Optical soliton perturbation with quadratic-cubic nonlinearity by the method of undetermined coefficients. J. Optoelectron. Adv. Mater. 19: 699-703.
  3. Asma M, Othman W A M, Wong B R and Biswas A, 2017. Optical soliton perturbation with quadratic-cubic nonlinearity by traveling wave hypothesis. Optoelectron. Adv. Mater. - Rapid Commun. 11: 517−519.
  4. Asma M, Othman W A M, Wong B R and Biswas A, 2019. Chirped optical Gausson perturbation with quadratic–cubic nonlinearity by collective variables. Opt. Quantum Electron. 51: 200. doi:10.1007/s11082-019-1878-9
  5. Astrakharchik G E and Malomed B A, 2018. Dynamics of one-dimensional quantum droplets. Phys. Rev. A. 98: 013631. doi:10.1103/PhysRevA.98.013631
  6. Biswas A, 2020. Quasi–monochromatic dynamics of optical solitons having quadratic–cubic nonlinearity. Phys. Lett. A. 384: 126528. doi:10.1016/j.physleta.2020.126528
  7. Biswas A, Sonmezoglu A, Ekici M, Alzahrani A K and Belic M R, 2020. Cubic–quartic optical solitons with differential group delay for Kudryashov’s model by extended trial function. J. Commun. Technol. Electron. 65: 1384-1398. doi:10.1134/S1064226920120037
  8. Fujioka J, Cortes E, Perez-Pascual R, Rodriguez R F, Espinosa A and Malomed B A, 2011. Chaotic solitons in the quadratic-cubic nonlinear Schrödinger equation under nonlinearity management. Chaos. 21: 033120. doi:10.1063/1.3629985
  9. Hayata K and Koshiba M, 1994. Prediction of unique solitary-wave polaritons in quadratic–cubic nonlinear dispersive media. J. Opt. Soc. Amer. B. 11: 2581-2585. doi:10.1364/JOSAB.11.002581
  10. Hayata K and Koshiba M, 1994. Kink solitons in quadratic-cubic nonlinear dispersive media. Phys. Rev. E. 50: 3267. doi:10.1103/PhysRevE.50.3267
  11. Khuri S A and Wazwaz A M, 2021. Soliton solutions through optical fibers for quadratic–cubic nonlinear medium: A complex ansätze approach. Optik. 229: 166268. doi:10.1016/j.ijleo.2021.166268
  12. Triki H, Biswas A, Moshokoa S P and Belic M, 2017. Optical solitons and conservation laws with quadratic-cubic nonlinearity. Optik. 128: 63-70. doi:10.1016/j.ijleo.2016.10.010
  13. Zayed E M E, El-Horbaty M and Alngar M E M, 2020. Cubic-quartic optical soliton perturbation having four laws non-linearity with a prolific integration algorithm. Optik. 220: 165121. doi:10.1016/j.ijleo.2020.165121
  14. Zayed E M E, Shohib R M A, Alngar M E M, Biswas A, Ekici M, Khan S, Alzahrani A K and Belic M R, 2021. Optical solitons and conservation laws associated with Kudryashov’s sextic power-law nonlinearity of refractive index. Ukr. J. Phys. Opt. 22: 38-49. doi:10.3116/16091833/22/1/38/2021
  15. Zayed E M E, Nofal T A, Alngar M E M and El-Horbaty M M, 2021. Cubic-quartic optical soliton perturbation in polarization-preserving fibers with complex Ginzburg-Landau equation having five nonlinear refractive index structures. Optik. 231: 166381. doi:10.1016/j.ijleo.2021.166381
  16. Kudryashov N A, 2020. Periodic and solitary waves in optical fiber Bragg gratings with dispersive reflectivity. Chin. J. Phys. 66: 401-405. doi:10.1016/j.cjph.2020.06.006
  17. Biswas A, 2020. Optical soliton cooling with polynomial law of nonlinear refractive index. J. Opt. 49: 580-583. doi:10.1007/s12596-020-00644-0
  18. Zayed E M E, Alngar M E M, Biswas A, Kara A H, Moraru L, Ekici M, Alzahrani A K and Belic M R, 2020. Solitons and conservation laws in magneto-optic waveguides with triple-power law nonlinearity. J. Opt. 49: 584-590. doi:10.1007/s12596-020-00650-2
  19. Zayed E M E, Al-Nowehy A G, Alngar M E M, Biswas A, Asma M, Ekici M, Alzahrani A K and Belic M R, 2021. Highly dispersive optical solitons in birefringent fibers with four nonlinear forms using Kudryashov’s approach. J. Opt. 50: 120-131. doi:10.1007/s12596-020-00668-6
  20. Vega-Guzman J, Biswas A, Asma M, Seadawy A R, Ekici M, Alzahrani A K and Belic M R, 2021. Optical soliton perturbation with parabolic–nonlocal combo nonlinearity: undetermined coefficients and semi-inverse variational principle. J. Opt. doi:10.1007/s12596-020-00670-y
  21. Gonzalez-Gaxiola O, Biswas A, Ekici M and Khan S, 2021. Highly dispersive optical solitons with quadratic–cubic law of refractive index by the variational iteration method. J. Opt. doi:10.1007/s12596-020-00671-x
  22. Yildirim Y, Biswas A, Kara A H, Ekici M, Alzahrani A K and Belic M R, 2021. Cubic–quartic optical soliton perturbation and conservation laws with generalized Kudryashov’s form of refractive index. J. Opt. 50: 354-360. doi:10.1007/s12596-021-00681-3
  23. Yildirim Y, Topkara E, Biswas A, Triki H, Ekici M, Guggilla P, Khan S and Belic M R, 2021. Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by sine-Gordon equation approach. J. Opt. 50: 322-329. doi:10.1007/s12596-021-00685-z
  24. Yildirim Y, Biswas A, Triki H, Ekici M, Guggilla P, Khan S, Moraru L and Belic M R, 2021. Cubic–quartic optical soliton perturbation with Kudryashov’s law of refractive index having quadrupled–power law and dual form of generalized nonlocal nonlinearity by sine-Gordon equation approach.J. Opt. 50: 593-599. doi:10.1007/s12596-021-00686-y
  25. Yildirim Y, Biswas A, Kara A H, Ekici M, Zayed E M E, Alzahrani A K and Belic M R, 2021. Optical solitons and conservation law with Kudryashov’s form of arbitrary refractive index. J. Opt. 50: 542–547. doi:10.1007/s12596-021-00688-w
(c) Ukrainian Journal of Physical Optics