A. G. Meshkov, V. V. Sokolov, “Integrable evolution equations with a constant separant”, Ufa Math. J., 4:3 (2012)

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Ufimskii Matematicheskii Zhurnal, 2012, Volume 4, Issue 3, Pages 104–154 (Mi ufa158)

This article is cited in 20 scientific papers (total in 20 papers)

Integrable evolution equations with a constant separant

A. G. Meshkov^a, V. V. Sokolov^b

^a Orel State Technical University, Orel, Russia
^b Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow. reg., Russia

Full-text PDF (995 kB) Citations (20)

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Abstract: The survey contains results of classification for integrable one-field evolution equations of orders 2, 3 and 5 with the constant separant. The classification is based on neccesary integrability conditions that follow from the existence of the formal recursion operator for integrable equations. Recursion formulas for the whole infinite sequence of these conditions are presented for the first time. The most of the classification statements can be found in papers by S. I. Svinilupov and V. V. Sokolov but the proofs never been published before. The result concerning the fifth order equations is stronger then obtained before.

Keywords: evolution differential equation, integrability, higher symmetry, conservation law, classification.

Received: 20.01.2012

Document Type: Article

UDC: 517.957

Language: Russian

Citation: A. G. Meshkov, V. V. Sokolov, “Integrable evolution equations with a constant separant”, Ufa Math. J., 4:3 (2012)

Citation in format AMSBIB

\Bibitem{MesSok12}

\by A.~G.~Meshkov, V.~V.~Sokolov

\paper Integrable evolution equations with a~constant separant

\jour Ufa Math. J.

\yr 2012

\vol 4

\issue 3

\mathnet{http://mi.mathnet.ru/eng/ufa158}

Linking options:

https://www.mathnet.ru/eng/ufa158

https://www.mathnet.ru/eng/ufa/v4/i3/p104

This publication is cited in the following 20 articles:

R. N. Garifullin, “Classification of semidiscrete equations of hyperbolic type. The case of fifth-order symmetries”, Theoret. and Math. Phys., 222:1 (2025), 10–19
R. N. Garifullin, “Classification of semidiscrete equations of hyperbolic type. The case of third-order symmetries”, Theoret. and Math. Phys., 217:2 (2023), 1767–1776
R. N. Garifullin, “On integrability of semi-discrete Tzitzeica equation”, Ufa Math. J., 13:2 (2021), 15–21
Garifullin R.N., Habibullin I.T., “Generalized Symmetries and Integrability Conditions For Hyperbolic Type Semi-Discrete Equations”, J. Phys. A-Math. Theor., 54:20 (2021), 205201
Igonin S., Manno G., “on Lie Algebras Responsible For Integrability of (1+1)-Dimensional Scalar Evolution Pdes”, J. Geom. Phys., 150 (2020), 103596
Carillo S., “Kdv-Type Equations Linked Via Backlund Transformations: Remarks and Perspectives”, Appl. Numer. Math., 141:SI (2019), 81–90
Igonin S., Manno G., “Lie Algebras Responsible For Zero-Curvature Representations of Scalar Evolution Equations”, J. Geom. Phys., 138 (2019), 297–316
Carillo S., Lo Schiavo M., Schiebold C., “Abelian Versus Non-Abelian Backlund Charts: Some Remarks”, Evol. Equ. Control Theory, 8:1, SI (2019), 43–55
R. N. Garifullin, R. I. Yamilov, “On the Integrability of a Lattice Equation with Two Continuum Limits”, J. Math. Sci. (N. Y.), 252:2 (2021), 283–289
Ufa Math. J., 9:3 (2017), 158–164
A. V. Bochkarev, A. I. Zemlyanukhin, “The geometric series method for constructing exact solutions to nonlinear evolution equations”, Comput. Math. Math. Phys., 57:7 (2017), 1111–1123
I. T. Habibullin, A. R. Khakimova, “On a Method For Constructing the Lax Pairs For Integrable Models Via a Quadratic Ansatz”, J. Phys. A-Math. Theor., 50:30 (2017), 305206
A. G. Meshkov, V. V. Sokolov, “On Third Order Integrable Vector Hamiltonian Equations”, J. Geom. Phys., 113 (2017), 206–214
V. E. Adler, “Integrability Test For Evolutionary Lattice Equations of Higher Order”, J. Symb. Comput., 74 (2016), 125–139
M. Yu. Balakhnev, “Differential Substitutions for Vectorial Generalizations of the mKdV Equation”, Math. Notes, 98:2 (2015), 204–209
Meshkov A.G., Sokolov V.V., “Integrable Hamiltonian Equations of Fifth Order With Hamiltonian Operator D-X”, Russ. J. Math. Phys., 22:2 (2015), 201–214
Meshkov A., Sokolov V., “Vector Hyperbolic Equations on the Sphere Possessing Integrable Third-Order Symmetries”, Lett. Math. Phys., 104:3 (2014), 341–360
V. E. Adler, “Necessary integrability conditions for evolutionary lattice equations”, Theoret. and Math. Phys., 181:2 (2014), 1367–1382
Meshkov A.G., Sokolov V.V., “Integrable Evolution Hamiltonian Equations of the Third Order With the Hamiltonian Operator D-X”, J. Geom. Phys., 85 (2014), 245–251
De Sole A., Kac V.G., “Non-Local Poisson Structures and Applications to the Theory of Integrable Systems”, Jap. J. Math., 8:2 (2013), 233–347

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

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