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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/tmf/v181/i3/p538
    • This publication is cited in the following 7 articles:
    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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