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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2008
• Main Authors: Meshkov, A.G., Balakhnev, M.Ju.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148971
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions / A.G. Meshkov, M.Ju. Balakhnev // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 45 назв. — англ.

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...