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

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 × 4 ma...

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Main Authors:	Maxim Ju. Balakhnev, Anatoly G. Meshkov
Format:	Article
Language:	English
Published:	National Academy of Science of Ukraine 2008-02-01
Series:	Symmetry, Integrability and Geometry: Methods and Applications
Subjects:	integrability symmetry conservation law differential substitutions zero curvature representation
Online Access:	http://dx.doi.org/10.3842/SIGMA.2008.018

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spelling	doaj-cb0626a0afbf406a957383f554d458b32020-11-24T23:08:34ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592008-02-014018Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential SubstitutionsMaxim Ju. BalakhnevAnatoly G. MeshkovA 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 × 4 matrices are presented.http://dx.doi.org/10.3842/SIGMA.2008.018integrabilitysymmetryconservation lawdifferential substitutionszero curvature representation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Maxim Ju. Balakhnev Anatoly G. Meshkov
spellingShingle	Maxim Ju. Balakhnev Anatoly G. Meshkov Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions Symmetry, Integrability and Geometry: Methods and Applications integrability symmetry conservation law differential substitutions zero curvature representation
author_facet	Maxim Ju. Balakhnev Anatoly G. Meshkov
author_sort	Maxim Ju. Balakhnev
title	Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions
title_short	Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions
title_full	Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions
title_fullStr	Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions
title_full_unstemmed	Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions
title_sort	two-field integrable evolutionary systems of the third order and their differential substitutions
publisher	National Academy of Science of Ukraine
series	Symmetry, Integrability and Geometry: Methods and Applications
issn	1815-0659
publishDate	2008-02-01
description	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 × 4 matrices are presented.
topic	integrability symmetry conservation law differential substitutions zero curvature representation
url	http://dx.doi.org/10.3842/SIGMA.2008.018
work_keys_str_mv	AT maximjubalakhnev twofieldintegrableevolutionarysystemsofthethirdorderandtheirdifferentialsubstitutions AT anatolygmeshkov twofieldintegrableevolutionarysystemsofthethirdorderandtheirdifferentialsubstitutions
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Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions

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