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Mat. Zametki, 2011, Volume 89, Issue 2, Pages 178–189 (Mi mz6644)  

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

First-Order Differential Substitutions for Equations Integrable on $\mathbb S^n$

M. Yu. Balakhnev

Orel State Technical University

Abstract: We determine necessary conditions under which integrable vector evolution equations of third order admit Miura-type transformations. For equations integrable on the $n$-dimensional sphere, we obtain first-order differential substitutions.

Keywords: vector evolution equation, Miura-type transformation, differential substitution, Bäcklund transformation, pseudosymmetry, Schwartz–KdV equation

DOI: https://doi.org/10.4213/mzm6644

Full text: PDF file (525 kB)
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English version:
Mathematical Notes, 2011, 89:2, 184–193

Bibliographic databases:

UDC: 517.957
Received: 13.01.2009
Revised: 22.06.2010

Citation: M. Yu. Balakhnev, “First-Order Differential Substitutions for Equations Integrable on $\mathbb S^n$”, Mat. Zametki, 89:2 (2011), 178–189; Math. Notes, 89:2 (2011), 184–193

Citation in format AMSBIB
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\by M.~Yu.~Balakhnev
\paper First-Order Differential Substitutions for Equations Integrable on~$\mathbb S^n$
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 2
\pages 178--189
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\crossref{https://doi.org/10.4213/mzm6644}
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\jour Math. Notes
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\vol 89
\issue 2
\pages 184--193
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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. M. Yu. Balakhnev, “Integrable Vector Isotropic Equations Admitting Differential Substitutions of First Order”, Math. Notes, 94:3 (2013), 307–313  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. S. Ya. Startsev, “On differential substitutions for evolution systems”, Ufa Math. J., 9:4 (2017), 108–113  mathnet  crossref  isi  elib
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