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.

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