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TMF, 2001, Volume 127, Number 1, Pages 47–62 (Mi tmf448)  

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

Symmetries of Systems of the Hyperbolic Riccati Type

A. A. Bormisov, F. Kh. Mukminov

Sterlitamak State Pedagogical Institute

Abstract: Let $\mathfrak G=\bigoplus_{i\in\mathbb Z}\mathfrak G_i$ be a Kac–Moody algebra, $U(x,y)$ be a function defined in $\mathfrak G_{-1}$, and $a$ be a constant element of $\mathfrak G_1$. We prove that the equation $U_{xy}=[[U,a],U_x]$ has two symmetry hierarchies connected by a gauge transformation. In particular, the well-known Konno equation appears in the case of the algebra $A_1^{(1)}$. The corresponding symmetry hierarchies contain the nonlinear Schrödinger and the Heisenberg magnet equations.

DOI: https://doi.org/10.4213/tmf448

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English version:
Theoretical and Mathematical Physics, 2001, 127:1, 446–459

Bibliographic databases:

Received: 05.10.2000

Citation: A. A. Bormisov, F. Kh. Mukminov, “Symmetries of Systems of the Hyperbolic Riccati Type”, TMF, 127:1 (2001), 47–62; Theoret. and Math. Phys., 127:1 (2001), 446–459

Citation in format AMSBIB
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\vol 127
\issue 1
\pages 446--459
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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. A. V. Zhiber, R. D. Murtazina, “On the characteristic Lie algebras for equations $u_{xy}=f(u,u_x)$”, J. Math. Sci., 151:4 (2008), 3112–3122  mathnet  crossref  mathscinet  zmath  elib  elib
    2. Habibullin, I, “On the classification of Darboux integrable chains”, Journal of Mathematical Physics, 49:10 (2008), 102702  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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