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TMF, 1982, Volume 51, Number 1, Pages 10–21 (Mi tmf2380)  

This article is cited in 49 scientific papers (total in 49 papers)

The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems

A. N. Leznov, V. G. Smirnov, A. B. Shabat

Abstract: The concept of the characteristic algebra of a system of equations of the form $u_{z\overline{z}}=F(u)$ is introduced. This algebra is associated with Lie–Bäcklund transformations. The conditions of integrability of such systems are formulated. It is shown that the case of integrability in quadrature corresponds to finite dimensionality of the characteristic algebra, while the case of integrability by the inverse scattering technique corresponds to this algebra's having a finite-dimensional representation. These requirements determine the form of the right-hand side $F$ for integrable systems.

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English version:
Theoretical and Mathematical Physics, 1982, 51:1, 322–330

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Received: 23.01.1981

Citation: A. N. Leznov, V. G. Smirnov, A. B. Shabat, “The group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems”, TMF, 51:1 (1982), 10–21; Theoret. and Math. Phys., 51:1 (1982), 322–330

Citation in format AMSBIB
\by A.~N.~Leznov, V.~G.~Smirnov, A.~B.~Shabat
\paper The~group of internal symmetries and the conditions of integrability of two-dimensional dynamical systems
\jour TMF
\yr 1982
\vol 51
\issue 1
\pages 10--21
\jour Theoret. and Math. Phys.
\yr 1982
\vol 51
\issue 1
\pages 322--330

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    This publication is cited in the following articles:
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