Ukrainian Journal of Physical Optics


2023 Volume 24, Issue 3


ISSN 1816-2002 (Online), ISSN 1609-1833 (Print)

Optical solitons for the concatenation model with power-law nonlinearity: undetermined coefficients

1,2,3,4Anjan Biswas, 5Jose M. Vega-Guzman, 6,7Yakup Yildirim, 8Seithuti P. Moshokoa, 4Maggie Aphane and 2Abdulah A. Alghamdi

1 Department of Mathematics and Physics, Grambling State University, Grambling, LA-71245, USA.
2 Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah-21589, Saudi Arabia.
3 Department of Applied Sciences, Cross-Border Faculty of Humanities, Economics and Engineering, Dunarea de Jos University of Galati, 111 Domneasca Street, Galati-800201, Romania.
4 Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa-0204, Pretoria, South Africa.
5 Department of Mathematics, Lamar University, Beaumont, TX-77710, USA.
6 Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey.
7 Department of Mathematics, Near East University, 99138 Nicosia, Cyprus.
8 Department of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa.

ABSTRACT

In the current paper, a full spectrum of 1–soliton solutions to the concatenation model with the power–law of self–phase modulation has been recovered. The method of undetermined coefficients has permitted us to solve this problem successfully. The parameter constraints naturally emerge from the derivation and are also listed, guaranteeing these solitons' existence. It has been proved that dark solitons and singular solitons of a specific type would exist only when the power–law parameter collapses to unity.

Keywords: solitons; power-law; concatenation; conservation laws

UDC: 535.32

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    3. Biswas A, Vega-Guzman J, Kara A H, Khan S, Triki H, Gonzalez-Gaxiola O, Moraru L & Georgescu P L, 2023. Optical solitons and conservation laws for the concatenation model: undetermined coefficients and multipliers approach. Universe, 9(1): 15. doi:10.3390/universe9010015
    4. Biswas A, Vega-Guzman J, Yildirim Y, Moraru L, Iticescu C & Alghamdi A A, 2023. Optical solitons for the concatenation model with differential group delay: undetermined coefficients. Mathematics. 11(9): 2012. doi:10.3390/math11092012
    5. Kudryashov N A, Biswas A, Borodina A G, Yildirim Y & Alshehri H M, 2023. Painleve analysis and optical solitons for a concatenated model. Optik. 272: 170255. doi:10.1016/j.ijleo.2022.170255
    6. Kukkar A, Kumar S, Malik S, Biswas A, Yildirim Y, Moshokoa S P, Khan S & Alghamdi A A, 2023. Optical solitons for the concatenation model with Kudryashov's approaches. Ukr.J.Phys.Opt. 24(2): 155-160. doi:10.3116/16091833/24/2/155/2023
    7. Triki H, Sun Y Q Zhou, Biswas A, Yildirim Y & Alshehri H M, 2022. Dark solitary pulses and moving fronts in an optical medium with the higher-order dispersive and nonlinear effects. Chaos Solit. Fractals. 164: 112622. doi:10.1016/j.chaos.2022.112622
    8. Wang M-Y, Biswas A, Yıldırım Y, Moraru L, Moldovanu S & Alshehri H M, 2023. Optical solitons for a concatenation model by trial equation approach. Electronics. 12(1): 19. doi:10.3390/electronics12010019
    9. Yildirim Y, Biswas A, Moraru L & Alghamdi A A, 2023. Quiescent optical solitons for the concatenation model with nonlinear chromatic dispersion. Mathematics. 11(7): 1709. doi:10.3390/math11071709

    Ця стаття відновлює повний спектр 1-солітонних розв’язків моделі конкатенації зі степеневим законом самофазової модуляції. Метод невизначених коефіцієнтів дозволив успішно вирішити цю проблему. Обмеження наведених параметрів природним чином виникає із виведення, що у свою чергу гарантує існування цих солітонів. Доведено, що темні солітони та сингулярні солітони певного типу існували б лише тоді, коли порядок степеневого закону спадав би до одиниці.

    Ключові слова: солітони; сила–закон; конкатенація; закони збереження

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