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Model. Anal. Inform. Sist., 2015, Volume 22, Number 6, Pages 795–817 (Mi mais475)  

This article is cited in 2 scientific papers (total in 2 papers)

Formal diagonalisation of Lax–Darboux schemes

A. V. Mikhailov

University of Leeds, School of Mathematics (Leeds, UK)

Abstract: We discuss the concept of Lax–Darboux scheme and illustrate it on well known examples associated with the Nonlinear Schrödinger (NLS) equation. We explore the Darboux links of the NLS hierarchy with the hierarchy of Heisenberg model, principal chiral field model as well as with differential-difference integrable systems (including the Toda lattice and differential-difference Heisenberg chain) and integrable partial difference systems. We show that there exists a transformation which formally diagonalises all elements of the Lax–Darboux scheme simultaneously. It provides us with generating functions of local conservation laws for all integrable systems obtained. We discuss the relations between conservation laws for systems belonging to the Lax–Darboux scheme.

Keywords: formal diagonalisation, Lax-Darboux schemes, nonlinear Schrödinger equation, NLS.

DOI: https://doi.org/10.18255/1818-1015-2015-6-795-817

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Bibliographic databases:

UDC: 51
Received: 28.11.2015
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Citation: A. V. Mikhailov, “Formal diagonalisation of Lax–Darboux schemes”, Model. Anal. Inform. Sist., 22:6 (2015), 795–817

Citation in format AMSBIB
\Bibitem{Mik15}
\by A.~V.~Mikhailov
\paper Formal diagonalisation of Lax--Darboux schemes
\jour Model. Anal. Inform. Sist.
\yr 2015
\vol 22
\issue 6
\pages 795--817
\mathnet{http://mi.mathnet.ru/mais475}
\crossref{https://doi.org/10.18255/1818-1015-2015-6-795-817}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3493712}
\elib{http://elibrary.ru/item.asp?id=25125096}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. T. Habibullin, A. R. Khakimova, “Invariant manifolds and Lax pairs for integrable nonlinear chains”, Theoret. and Math. Phys., 191:3 (2017), 793–810  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. Ufa Math. J., 9:3 (2017), 158–164  mathnet  crossref  mathscinet  isi  elib  elib
  • Моделирование и анализ информационных систем
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