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Ufa Mathematical Journal, 2023, Volume 15, Issue 1, Pages 122–20
DOI: https://doi.org/10.13108/2023-15-1-122
(Mi ufa646)
 

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

Integrable Tolkynay equations and related Yajima-Oikawa type equations

Zh. Myrzakulovaab, G. Nugmanovaab, N. Serikbayevab, K. Yesmakhanovaba, R. Myrzakulovab

a Eurasian National University, Satbayev str. 2, 010008, Astana, Kazakhstan
b Ratbay Myrzakulov Eurasian International Centre for Theoretical Physics, 38th str., 27/1, 010009, Astana, Kazakhstan
References:
Abstract: We consider some nonlinear models describing resonance interactions of long waves and short-waves (shortly, the LS waves models). Such LS models were derived and proposed due to various motivations, which mainly come from the different branches of modern physics, especially, from the fluid and plasma physics. In this paper, we study some of integrable LS models, namely, the Yajima-Oikawa equation, the Newell equation, the Ma equation, the Geng-Li equation and their different modifications and extensions. In particular, the gauge equivalent counterparts of these integrable LS models (equations), namely, different integrable spin systems are constructed. In fact, these gauge equivalent counterparts of these LS equations are integrable generalized Heisenberg ferromagnet type models (equations) (HFE) with self-consistent potentials (HFESCP). The associated Lax representations of these HFESCP are presented. Using these Lax representations of these HFESCP, they can be studied by the inverse scattering method. For instance, the equivalence established using the Lax representation also makes it possible to find a connection between the solutions of the corresponding integrable equations.
Keywords: Integrable equations, Heisenberg ferromagnet equation, Yajima-Oikawa equation, gauge equivalent, Lax representation.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan AP14971227
This work was supported by the Ministry of Science and Higher Education of the Republic of Kazakhstan, Grant AP14971227.
Received: 15.08.2020
Bibliographic databases:
Document Type: Article
UDC: 517.951, 517.957
MSC: 35C08, 35Q51
Language: English
Original paper language: English
Citation: Zh. Myrzakulova, G. Nugmanova, N. Serikbayev, K. Yesmakhanova, R. Myrzakulov, “Integrable Tolkynay equations and related Yajima-Oikawa type equations”, Ufa Math. J., 15:1 (2023), 122–20
Citation in format AMSBIB
\Bibitem{MyrNugSer23}
\by Zh.~Myrzakulova, G.~Nugmanova, N.~Serikbayev, K.~Yesmakhanova, R.~Myrzakulov
\paper Integrable Tolkynay equations and related Yajima-Oikawa type equations
\jour Ufa Math. J.
\yr 2023
\vol 15
\issue 1
\pages 122--20
\mathnet{http://mi.mathnet.ru//eng/ufa646}
\crossref{https://doi.org/10.13108/2023-15-1-122}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4575923}
Linking options:
  • https://www.mathnet.ru/eng/ufa646
  • https://doi.org/10.13108/2023-15-1-122
  • https://www.mathnet.ru/eng/ufa/v15/i1/p122
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Уфимский математический журнал
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    Abstract page:113
    Russian version PDF:31
    English version PDF:65
    References:26
     
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