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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 206, Number 2, Pages 149–163
DOI: https://doi.org/10.4213/tmf9953 (Mi tmf9953) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Binary Darboux transformation for a negative-order AKNS equation

Z. Amjad, D. Khan

Department of Physics, University of the Punjab, Lahore, Pakistan
Full-text PDF (763 kB) Citations (5)
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DOI: https://doi.org/10.4213/tmf9953
Abstract: We study a binary Darboux transformation for a negative-order AKNS equation. Iterating the transformation, we obtain $N$-fold quasi-Grammian solutions expressed in terms of quasideterminants. In some simple cases, we construct explicit solutions of the studied equation with nonvanishing and vanishing backgrounds including bright and dark breathers, a soliton, and solutions with one and two humps.
Keywords: soliton, integrable system, Darboux transformation, binary Darboux transformation, quasideterminant.
Received: 06.07.2020
Revised: 05.10.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 206, Issue 2, Pages 128–141
DOI: https://doi.org/10.1134/S0040577921020021
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Z. Amjad, D. Khan, “Binary Darboux transformation for a negative-order AKNS equation”, TMF, 206:2 (2021), 149–163; Theoret. and Math. Phys., 206:2 (2021), 128–141
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf9953
  • https://doi.org/10.4213/tmf9953
  • https://www.mathnet.ru/eng/tmf/v206/i2/p149
    • This publication is cited in the following 5 articles:
    1. A. Mirza, M. ul Hassan, “Superfield Bäcklund and Darboux transformations of an $\mathcal N=1$ supersymmetric coupled dispersionless integrable system”, Theoret. and Math. Phys., 219:1 (2024), 629–637  mathnet  crossref  crossref  mathscinet  adsnasa
    2. Zeeshan Amjad, Bushra Haider, Wen-Xiu Ma, “Integrable Discretization and Multi-soliton Solutions of Negative Order AKNS Equation”, Qual. Theory Dyn. Syst., 23:S1 (2024)  crossref
    3. R. Ye, Y. Zhang, “A vectorial Darboux transformation for the Fokas–Lenells system”, Chaos, Solitons & Fractals, 169 (2023), 113233  crossref  mathscinet
    4. F. Müller-Hoissen, “A vectorial binary Darboux transformation for the first member of the negative part of the AKNS hierarchy”, J. Phys. A: Math. Theor., 56:12 (2023), 125701  crossref  mathscinet
    5. Z. Amjad, “Breather and soliton solutions of semi-discrete negative order AKNS equation”, Eur. Phys. J. Plus, 137:9 (2022)  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    Abstract page:251
    Full-text PDF :42
    References:63
    First page:8
     
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