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SIGMA, 2008, Volume 4, 018, 29 pages (Mi sigma271)  

This article is cited in 9 scientific papers (total in 9 papers)

Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions

Anatoly G.G. Meshkov, Maxim Ju. Balakhnev

Orel State Technical University, Orel, Russia

Abstract: A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of them. Examples of zero curvature representations with $4\times4$ matrices are presented.

Keywords: integrability; symmetry; conservation law; differential substitutions; zero curvature representation

DOI: https://doi.org/10.3842/SIGMA.2008.018

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Full text: http://emis.mi.ras.ru/.../018
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Bibliographic databases:

ArXiv: 0802.1253
MSC: 37K10; 35Q53; 37K20
Received: October 4, 2007; in final form January 17, 2008; Published online February 9, 2008
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Citation: Anatoly G.G. Meshkov, Maxim Ju. Balakhnev, “Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions”, SIGMA, 4 (2008), 018, 29 pp.

Citation in format AMSBIB
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\by Anatoly G.G.~Meshkov, Maxim Ju.~Balakhnev
\paper Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions
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\yr 2008
\vol 4
\papernumber 018
\totalpages 29
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mikhailov A. V., Sokolov V. V., “Symmetries of differential equations and the problem of integrability”, Lecture Notes in Physics, 767, 2009, 19–88  crossref  mathscinet  zmath  scopus
    2. M. Yu. Balakhnev, “First-Order Differential Substitutions for Equations Integrable on $\mathbb S^n$”, Math. Notes, 89:2 (2011), 184–193  mathnet  crossref  crossref  mathscinet  isi
    3. A. G. Meshkov, V. V. Sokolov, “Integriruemye evolyutsionnye uravneniya s postoyannoi separantoi”, Ufimsk. matem. zhurn., 4:3 (2012), 104–154  mathnet
    4. Balakhnev M.Yu., Demskoi D.K., “Auto-Backlund Transformations and Superposition Formulas for Solutions of Drinfeld-Sokolov Systems”, Appl. Math. Comput., 219:8 (2012), 3625–3637  crossref  mathscinet  zmath  isi  elib  scopus
    5. M. Yu. Balakhnev, “Differential Substitutions for Vectorial Generalizations of the mKdV Equation”, Math. Notes, 98:2 (2015), 204–209  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Wang D.-Sh., Wei X., “Integrability and Exact Solutions of a Two-Component Korteweg-de Vries System”, Appl. Math. Lett., 51 (2016), 60–67  crossref  mathscinet  zmath  isi  elib  scopus
    7. Wang D.-Sh., Liu J., Zhang Zh., “Integrability and equivalence relationships of six integrable coupled Korteweg-de Vries equations”, Math. Meth. Appl. Sci., 39:12 (2016), 3516–3530  crossref  mathscinet  zmath  isi  elib  scopus
    8. Berkeley G., Igonin S., “Miura-type transformations for lattice equations and Lie group actions associated with Darboux?Lax representations”, J. Phys. A-Math. Theor., 49:27 (2016), 275201  crossref  mathscinet  zmath  isi  elib  scopus
    9. Lou S.Y., “Alice-Bob Systems, (P)Over-Cap-(T)Over-Cap-(C)Over-Cap Symmetry Invariant and Symmetry Breaking Soliton Solutions”, J. Math. Phys., 59:8 (2018), 083507  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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