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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 181, Number 3, Pages 538–552
DOI: https://doi.org/10.4213/tmf8758 (Mi tmf8758) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Hirota difference equation: Inverse scattering transform, Darboux transformation, and solitons

A. K. Pogrebkovab

a Steklov Mathematical Institute, RAS Moscow, Russia
b National Research University "Higher School of Economics", Moscow, Russia
Full-text PDF (433 kB) Citations (7)
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DOI: https://doi.org/10.4213/tmf8758
Abstract: We consider the direct and inverse problems for the Hirota difference equation. We introduce the Jost solutions and scattering data and describe their properties. In a special case, we show that the Darboux transformation allows finding the evolution in discrete time and obtaining a recursive procedure for sequentially constructing the Jost solution at an arbitrary time for a given initial value. We consider some properties of the soliton solutions.
Keywords: Hirota difference equation, inverse scattering transform, soliton, Darboux transformation.
Funding agency Grant number
Russian Foundation for Basic Research 13-01-12405
14-01-00860
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 01.07.2014
English version:
Theoretical and Mathematical Physics, 2014, Volume 181, Issue 3, Pages 1585–1598
DOI: https://doi.org/10.1007/s11232-014-0237-z
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. K. Pogrebkov, “Hirota difference equation: Inverse scattering transform, Darboux transformation, and solitons”, TMF, 181:3 (2014), 538–552; Theoret. and Math. Phys., 181:3 (2014), 1585–1598
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf8758
  • https://doi.org/10.4213/tmf8758
  • https://www.mathnet.ru/eng/tmf/v181/i3/p538
    • This publication is cited in the following 7 articles:
    1. H. W. A. Riaz, Aamir Farooq, “A (2+1) modified KdV equation with time-dependent coefficients: exploring soliton solution via Darboux transformation and artificial neural network approach”, Nonlinear Dyn, 2024  crossref
    2. H W A Riaz, Aamir Farooq, “Solitonic solutions for the reduced Maxwell-Bloch equations via the Darboux transformation and artificial neural network in nonlinear wave dynamics”, Phys. Scr., 99:12 (2024), 126010  crossref
    3. A. Pogrebkov, “Hirota difference equation and Darboux system: mutual symmetry”, Symmetry-Basel, 11:3 (2019), 436  crossref  isi
    4. Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.  mathnet  crossref  mathscinet
    5. T. C. Kofane, M. Fokou, A. Mohamadou, E. Yomba, “Lump solutions and interaction phenomenon to the third-order nonlinear evolution equation”, Eur. Phys. J. Plus, 132:11 (2017), 465  crossref  isi  scopus
    6. L.-L. Song, Zh.-L. Pu, Zh.-D. Dai, “Spatio-temporal deformation of kink-breather to the (2+1)-dimensional potential Boiti–Leon–Manna–Pempinelli equation”, Commun. Theor. Phys., 67:5 (2017), 493–497  crossref  mathscinet  zmath  isi  scopus
    7. Yu.-F. Liu, R. Guo, H. Li, “Breathers and localized solutions of complex modified Korteweg–de Vries equation”, Mod. Phys. Lett. B, 29:23 (2015), 1550129  crossref  mathscinet  adsnasa  isi  elib  scopus
    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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