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TMF, 2014, Volume 181, Number 3, Pages 538–552 (Mi tmf8758)  

This article is cited in 5 scientific papers (total in 5 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

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


DOI: https://doi.org/10.4213/tmf8758

Full text: PDF file (433 kB)
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English version:
Theoretical and Mathematical Physics, 2014, 181:3, 1585–1598

Bibliographic databases:

Received: 01.07.2014

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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  • http://mi.mathnet.ru/eng/tmf/v181/i3/p538

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. Andrei K. Pogrebkov, “Symmetries of the Hirota Difference Equation”, SIGMA, 13 (2017), 053, 14 pp.  mathnet  crossref  mathscinet
    3. 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
    4. 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
    5. Pogrebkov A., “Hirota Difference Equation and Darboux System: Mutual Symmetry”, Symmetry-Basel, 11:3 (2019), 436  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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