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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 214, Number 2, Pages 224–238
DOI: https://doi.org/10.4213/tmf10347 (Mi tmf10347) 		 
Noncommutative generalization and quasi-Gramian solutions of the Hirota equation

H.  Wajahat  A. Riaz

School of Science, China University of Mining and Technology, Beijing, China
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DOI: https://doi.org/10.4213/tmf10347
Abstract: The nonlinear Schrödinger (NLS) and modified Korteweg–de Vries (mKdV) equations can be combined to form an integrable equation known as the Hirota equation. In this paper, we investigate a noncommutative generalization of the Hirota equation by establishing the zero-curvature condition, identifying the Lax pair, and using the covariance strategy to find the binary Darboux transformation (DT) and the Darboux transformation (DT) for the noncommutative Hirota equation. We also construct the quasi-Gramian solutions. First-order single- and double-peaked solutions in noncommutative contexts are also presented.
Keywords: noncommutative integrable system, Darboux transformation, binary Darboux transformation, soliton.
Funding agency Grant number
National Natural Science Foundation of China 11871471
11331008
11931017
Foreign Experts Scientific Cooperation Fund
This work was supported by the National Natural Science Foundation of China (grant Nos. 11871471, 11331008, and 11931017) and the Foreign Experts Scientific Cooperation Fund.
Received: 07.08.2022
Revised: 15.09.2022
English version:
Theoretical and Mathematical Physics, 2023, Volume 214, Issue 2, Pages 194–206
DOI: https://doi.org/10.1134/S0040577923020046
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: H.  Wajahat  A. Riaz, “Noncommutative generalization and quasi-Gramian solutions of the Hirota equation”, TMF, 214:2 (2023), 224–238; Theoret. and Math. Phys., 214:2 (2023), 194–206
Citation in format AMSBIB
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\paper Noncommutative generalization and quasi-Gramian solutions of the~Hirota equation
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\pages 224--238
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\jour Theoret. and Math. Phys.
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\pages 194--206
\crossref{https://doi.org/10.1134/S0040577923020046}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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