Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 4 (2008), 018, 29 pages      arXiv:0802.1253      https://doi.org/10.3842/SIGMA.2008.018

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

Anatoly G. Meshkov and Maxim Ju. Balakhnev
Orel State Technical University, Orel, Russia

Received October 04, 2007, in final form January 17, 2008; Published online February 09, 2008

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 × 4 matrices are presented.

Key words: integrability; symmetry; conservation law; differential substitutions; zero curvature representation.

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