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Authors = Abdul H. Kara

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10 pages, 811 KiB  
Communication
Optical Solitons and Conservation Laws for the Concatenation Model: Undetermined Coefficients and Multipliers Approach
by Anjan Biswas, Jose Vega-Guzman, Abdul H. Kara, Salam Khan, Houria Triki, O. González-Gaxiola, Luminita Moraru and Puiu Lucian Georgescu
Universe 2023, 9(1), 15; https://doi.org/10.3390/universe9010015 - 27 Dec 2022
Cited by 47 | Viewed by 2409
Abstract
This paper retrieves an optical 1–soliton solution to a model that is written as a concatenation of the Lakshmanan–Porsezian–Daniel model and Sasa–Satsuma equation. The method of undetermined coefficients obtains a full spectrum of 1–soliton solutions. The multiplier approach yields the conserved densities, which [...] Read more.
This paper retrieves an optical 1–soliton solution to a model that is written as a concatenation of the Lakshmanan–Porsezian–Daniel model and Sasa–Satsuma equation. The method of undetermined coefficients obtains a full spectrum of 1–soliton solutions. The multiplier approach yields the conserved densities, which subsequently lead to the conserved quantities from the bright 1–soliton solution. Full article
(This article belongs to the Special Issue Research on Optical Soliton Perturbation)
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12 pages, 2586 KiB  
Article
Shallow Water Waves and Conservation Laws with Dispersion Triplet
by Anjan Biswas, Nyah Coleman, Abdul H. Kara, Salam Khan, Luminita Moraru, Simona Moldovanu, Catalina Iticescu and Yakup Yıldırım
Appl. Sci. 2022, 12(7), 3647; https://doi.org/10.3390/app12073647 - 5 Apr 2022
Cited by 7 | Viewed by 1934
Abstract
This paper secures solitary waves and conservation laws to the familiar Korteweg–de Vries equation and Gardner’s equation with three dispersion sources. The traveling wave hypothesis leads to the emergence of such waves. The three sources of dispersion are spatial dispersion, spatio–temporal dispersion and [...] Read more.
This paper secures solitary waves and conservation laws to the familiar Korteweg–de Vries equation and Gardner’s equation with three dispersion sources. The traveling wave hypothesis leads to the emergence of such waves. The three sources of dispersion are spatial dispersion, spatio–temporal dispersion and the dual-emporal–spatial dispersion. The conservation laws are enumerated for these models, evolved from the multiplier approach. The conserved quantities are computed with the solitary wave solutions that were recovered. Full article
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