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

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Teoreticheskaya i Matematicheskaya Fizika, 1986, Volume 66, Number 1, Pages 47–65 (Mi tmf4593)

This article is cited in 15 scientific papers (total in 15 papers)

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

Full-text PDF (1825 kB) Citations (15)

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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.

Received: 16.01.1985

English version:
Theoretical and Mathematical Physics, 1986, Volume 66, Issue 1, Pages 31–44
DOI: https://doi.org/10.1007/BF01028936

Bibliographic databases:

Language: Russian

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

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$u_t=A(u)u_{xx}+F(u,u_x)$.~II

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\jour Theoret. and Math. Phys.

\yr 1986

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Linking options:

https://www.mathnet.ru/eng/tmf4593

https://www.mathnet.ru/eng/tmf/v66/i1/p47

Cycle of papers

Integrability conditions for systems of two equations of the form $u_t+A(u)u_{xx}+F(u,u_x)$ . I
A. V. Mikhailov, A. B. Shabat
TMF, 1985, 62:2, 163–185
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
TMF, 1986, 66:1, 47–65

This publication is cited in the following 15 articles:

Ndogmo J.C., “Integrable Classes of a Family of Evolution Equations”, J. Math. Phys., 63:1 (2022), 011510
Adler V.E. Sokolov V.V., “Non-Abelian Evolution Systems With Conservation Laws”, Math. Phys. Anal. Geom., 24:1 (2021), 7
A.V. Mikhailov, V.V. Sokolov, Lecture Notes in Physics, 767, Integrability, 2009, 19
Novikov, VS, “Symmetry structure of integrable nonevolutionary equations”, Studies in Applied Mathematics, 119:4 (2007), 393
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
A. M. Agalarov, R. M. Magomedmirzaev, “Nontrivial class of composite $U(\sigma+\mu)$ vector solitons”, JETP Letters, 76:7 (2002), 414–418
A. V. Mikhailov, A. B. Shabat, V. V. Sokolov, Springer Series in Nonlinear Dynamics, What Is Integrability?, 1991, 115
R. K. Dodd, “Fundamental representations of the m-principal realization of g l∞”, Journal of Mathematical Physics, 31:3 (1990), 533
O. I. Mokhov, “Commuting differential operators of rank 3, and nonlinear differential equations”, Math. USSR-Izv., 35:3 (1990), 629–655
Mauro L. Rabelo, “On Equations Which Describe Pseudospherical Surfaces”, Stud Appl Math, 81:3 (1989), 221
P. A. Clarkson, A. S. Fokas, M J. Ablowitz, “Hodograph Transformations of Linearizable Partial Differential Equations”, SIAM J. Appl. Math., 49:4 (1989), 1188
V. P. Gerdt, A. B. Shabat, S. I. Svinolupov, A.Yu. Zharkov, Lecture Notes in Computer Science, 378, Eurocal '87, 1989, 81
V. V. Sokolov, “On the symmetries of evolution equations”, Russian Math. Surveys, 43:5 (1988), 165–204
A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, “Extension of the module of invertible transformations. Classification of integrable systems”, Commun.Math. Phys., 115:1 (1988), 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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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