Ukrainian Journal of Physical Optics 

Volume 22, Issue 1, 2021
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Optical solitons and conservation laws associated with Kudryashov’s sextic power-law nonlinearity of refractive index.

1Elsayed M. E. Zayed, 1Reham M. A. Shohib, 1Mohamed E. M. Alngar, 2,3,4,5Anjan Biswas, 6Mehmet Ekici, 2Salam Khan, 3Abdullah Khamis Alzahrani and 7Milivoj R. Belic 

1Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519,   Egypt 
2Department of Physics, Chemistry and Mathematics, Alabama A&M University,   Normal, AL 35762–4900, USA 
3Mathematical Modeling and Applied Computation (MMAC) Research Group,    Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi   Arabia
4Department of Applied Mathematics, National Research Nuclear University, 31   Kashirskoe Highway, Moscow 115409, Russian Federation
5Department of Mathematics and Applied Mathematics, Sefako Makgatho Health   Sciences University, Medunsa 0204, Pretoria, South Africa
6Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok   University, 66100 Yozgat, Turkey 
7Science Program, Texas A&M University at Qatar, PO Box 23874, Doha, Qatar
 
 

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Abstract. We recover the cases of solutions in the shape of bright, dark and singular optical solitons for the self-phase modulation effect, which belongs to the type of N. A. Kudryashov’s sextic power-law nonlinearity of refractive index. Three different integration schemes have been implemented. These are a unified Riccati equation, our new mapping scheme and our addendum to the common N. A. Kudryashov’s method. All of the solitons are enlisted and the criterions of their existence are mentioned. Finally, we extract three appropriate conservation laws.

Keywords: refractive index, sextic -power nonlinearities, Kudryashov’s method, solitons

UDC: 535.32
Ukr. J. Phys. Opt. 22 38-49
doi: 10.3116/16091833/22/1/38/2021
Received: 10.10.2020

Анотація. Одержано розв’язки у вигляді «яскравих», «темних» і сингулярних оптичних солітонів для ефекту самофазної модуляції, який належить до типу степеневої нелінійності показника заломлення шостого порядку, що була раніше описана Н. А. Кудряшовим. Впроваджено три різні схеми інтегрування. Це уніфіковане рівняння Ріккаті, наш новий метод відображення та розвиток загальноприйнятого методу Н. А. Кудряшова. Наведено вирази для всіх солітонів та перераховано критерії їхнього існування. Одержано також три відповідні закони збереження.

Ключові слова: коефіцієнт заломлення, нелінійності шостого порядку, метод Кудряшова, солітони
REFERENCES
  1. 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
  2. Biswas A, Ekici M, Zhou Q, Alzahrani A K and Belic M, 2020. Conservation laws for optical solitons with polynomial and triple-power laws of refractive index. Optik. 202: 163476. doi:10.1016/j.ijleo.2019.163476
  3. Jawad A J M, Abu-Al Shaeer M J, Zayed E M E, Alngar M E M, Biswas A, Ekici M, Alzahrani A K and Belic M R, 2020. Optical soliton perturbation with exotic forms of nonlinear refractive index. Optik. 223: 165329. doi:10.1016/j.ijleo.2020.165329
  4. Kaur G, Kaur G and Sharma S, 2020. New dispersion-compensated Raman-amplifier cascade with a single-pump parametric amplifier for dense wavelength-division multiplexing. Ukr. J. Phys. Opt. 21: 35-46. doi:10.3116/16091833/21/1/35/2020
  5. Kohl R W, Biswas A, Zhou Q, Ekici M, Alzahrani A K and Belic M R, 2020. Optical soliton perturbation with polynomial and triple-power laws of refractive index by semi-inverse variational principle. Chaos Solit. Fract. 135: 109765. doi:10.1016/j.chaos.2020.109765
  6. Kudryashov N A, 2019. First integrals and general solution of the traveling wave reduction for Schrödinger equation with anti-cubic nonlinearity. Optik. 185: 665−671. doi:10.1016/j.ijleo.2019.03.167
  7. Kudryashov N A, 2019. General solution of traveling wave reduction for the Kundu-Mukherjee-Naskar model. Optik. 186: 22-27. doi:j.ijleo.2019.04.072
  8. Kudryashov N A, 2019. First integrals and general solution of the Fokas-Lenells equation. Optik. 195: 163135. doi:10.1016/j.ijleo.2019.163135
  9. Kudryashov N A, 2020. Mathematical model of propagation pulse in optical fiber with power nonlinearities. Optik. 212: 164750. doi:10.1016/j.ijleo.2020.164750
  10. Kudryashov N A, 2019. A generalized model for description of propagation pulses in optical fiber. Optik. 189: 42-52. doi:10.1016/j.ijleo.2019.05.069
  11. Kudryashov N A and Antonova E V, 2020. Solitary waves of equation for propagation pulse with power nonlinearities. Optik. 217: 164881. doi:10.1016/j.ijleo.2020.164881
  12. Kudryashov N A, 2020. Method for finding highly dispersive optical solitons of nonlinear differential equations. Optik. 206: 163550. doi:10.1016/j.ijleo.2019.163550
  13. Kudryashov N A, 2020. Highly dispersive optical solitons of equation with various polynomial nonlinearity law. Chaos Solit. Fract. 140: 110202. doi:10.1016/j.chaos.2020.110202
  14. 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
  15. Kudryashov N A, 2020. First integrals and general solution of the complex Ginzburg-Landau equation. Appl. Math. Comput. 386: 125407. doi:10.1016/j.amc.2020.125407
  16. Kudryashov N A, 2020. Optical solitons of the model with arbitrary refractive index. Optik. 224: 165391. doi:10.1016/j.ijleo.2020.165391
  17. Sirendaoreji N, 2017. Unified Riccati equation expansion method and its application to two new classes of Benjamin-Bona-Mahony equations. Nonlin. Dyn. 89: 333-344. doi:10.1007/s11071-017-3457-6
  18. Zeng X and Yong X, 2008. A new mapping method and its applications to nonlinear partial differential equations. Phys. Lett. A. 372: 6602-6607. doi:10.1016/j.physleta.2008.09.025
  19. 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
  20. Zhidkov P E. Korteweg-de Vries and nonlinear Schrödinger equations: qualitative theory. Springer Verlag: New York (2001).
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