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Teoreticheskaya i Matematicheskaya Fizika, 2022, Volume 213, Number 1, Pages 20–40
DOI: https://doi.org/10.4213/tmf10267
(Mi tmf10267)
 

This article is cited in 3 scientific papers (total in 3 papers)

On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems

V. S. Gerdjikovab, Nianhua Lic, V. B. Matveevde, A. O. Smirnovf

a Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
b Institute for Advanced Physical Studies, Sofia, Bulgaria
c School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, China
d Institut de Mathématiques de Bourgogne (IMB), Dijon, France
e St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
f Saint-Petersburg State University of Aerospace Instrumentation
Full-text PDF (568 kB) Citations (3)
References:
Abstract: We consider a simplest two-dimensional reduction of the remarkable three-dimensional Hirota–Ohta system. The Lax pair of the Hirota–Ohta system was extended to a Lax triad by adding extra third linear equation, whose compatibility conditions with the Lax pair of the Hirota–Ohta imply another remarkable systems: the Kulish–Sklyanin system (KSS) together with its first higher commuting flow, which we can call the vector complex mKdV. This means that any common particular solution of both these two-dimensional integrable systems yields a corresponding particular solution of the three-dimensional Hirota–Ohta system. Using the Zakharov–Shabat dressing method, we derive the $N$-soliton solutions of these systems and analyze their interactions, i.e., explicitly derive the shifts of the relative center-of-mass coordinates and the phases as functions of the discrete eigenvalues of the Lax operator. Next, we relate Hirota–Ohta-type system to these nonlinear evolution equations and obtain its $N$-soliton solutions.
Keywords: two-dimensional Kulish–Sklyanin system, three-dimensional Hirota–Ohta system, Lax representation, dressing method, multisoliton solutions, two-dimensional reductions.
Funding agency Grant number
Russian Foundation for Basic Research 21-51-53017
Bulgarian National Science Fund KP-06N42-2
Ministry of Science and Higher Education of the Russian Federation FSRF-2020-0004
The research of V. B. Matveev and Nianhua Li was funded by RFBR and NSFC, project No. 21-51-53017. V. S. Gerdjikov has been supported in part by the Bulgarian Science Foundation, contract KP-06N42-2. The work of A. O. Smirnov has been supported by the Ministry of Science and Higher Education of the Russian Federation (grant agreement No. FSRF-2020-0004).
Received: 05.02.2022
Revised: 05.02.2022
English version:
Theoretical and Mathematical Physics, 2022, Volume 213, Issue 1, Pages 1331–1347
DOI: https://doi.org/10.1134/S0040577922100038
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. S. Gerdjikov, Nianhua Li, V. B. Matveev, A. O. Smirnov, “On soliton solutions and soliton interactions of Kulish–Sklyanin and Hirota–Ohta systems”, TMF, 213:1 (2022), 20–40; Theoret. and Math. Phys., 213:1 (2022), 1331–1347
Citation in format AMSBIB
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\by V.~S.~Gerdjikov, Nianhua~Li, V.~B.~Matveev, A.~O.~Smirnov
\paper On soliton solutions and soliton interactions of Kulish--Sklyanin and Hirota--Ohta systems
\jour TMF
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\issue 1
\pages 20--40
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\crossref{https://doi.org/10.4213/tmf10267}
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\transl
\jour Theoret. and Math. Phys.
\yr 2022
\vol 213
\issue 1
\pages 1331--1347
\crossref{https://doi.org/10.1134/S0040577922100038}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85140455108}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Теоретическая и математическая физика Theoretical and Mathematical Physics
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