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 TMF, 1986, Volume 66, Number 1, Pages 47–65 (Mi tmf4593)

Integrability conditions for systems of two equations of the form $u_t=A(u)u_{xx}+F(u,u_x)$. II

A. V. Mikhailov, A. B. Shabat

Abstract: The conditions (integrability conditions) that the right-hand side of any system of equations of the form indicated in the title must satisfy if the system is to have a rich set of conservation laws are found. The iutegrability conditions form an overdetermined system of nonlinear partial differential equations. This overdetermined system of equations can be integrated by quadrature and the form of the right-hand side completely determined.

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English version:
Theoretical and Mathematical Physics, 1986, 66:1, 31–44

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Citation: A. V. Mikhailov, A. B. Shabat, “Integrability conditions for systems of two equations of the form $u_t=A(u)u_{xx}+F(u,u_x)$. II”, TMF, 66:1 (1986), 47–65; Theoret. and Math. Phys., 66:1 (1986), 31–44

Citation in format AMSBIB
\Bibitem{MikSha86} \by A.~V.~Mikhailov, A.~B.~Shabat \paper Integrability conditions for systems of two equations of the form $u_t=A(u)u_{xx}+F(u,u_x)$.~II \jour TMF \yr 1986 \vol 66 \issue 1 \pages 47--65 \mathnet{http://mi.mathnet.ru/tmf4593} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=831417} \zmath{https://zbmath.org/?q=an:0606.35042} \transl \jour Theoret. and Math. Phys. \yr 1986 \vol 66 \issue 1 \pages 31--44 \crossref{https://doi.org/10.1007/BF01028936} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1986D593000004} 

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This publication is cited in the following articles:
1. A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, “The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems”, Russian Math. Surveys, 42:4 (1987), 1–63
2. V. V. Sokolov, “On the symmetries of evolution equations”, Russian Math. Surveys, 43:5 (1988), 165–204
3. O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Math. USSR-Izv., 35:3 (1990), 629–655
4. A. M. Agalarov, R. M. Magomedmirzaev, “Nontrivial class of composite $U(\sigma+\mu)$ vector solitons”, JETP Letters, 76:7 (2002), 414–418
5. Tsuchida, T, “Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I”, Journal of Physics A-Mathematical and General, 38:35 (2005), 7691
6. Novikov, VS, “Symmetry structure of integrable nonevolutionary equations”, Studies in Applied Mathematics, 119:4 (2007), 393
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