Abstract:
The concept of the characteristic algebra of a system of equations of the form uz¯¯¯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.
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
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\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
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\jour Theoret. and Math. Phys.
\yr 1982
\vol 51
\issue 1
\pages 322--330
\crossref{https://doi.org/10.1007/BF01029257}
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Linking options:
https://www.mathnet.ru/eng/tmf2380
https://www.mathnet.ru/eng/tmf/v51/i1/p10
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