Anatoly G.G. Meshkov, Maxim Ju. Balakhnev, “Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions”, SIGMA, 2008, Volume 4,018, 29 pp.

This article is cited in 10 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.

MSC: 37K10; 35Q53; 37K20

Received: October 4, 2007; in final form January 17, 2008; Published online February 9, 2008

Language: English

DOI: 10.3842/SIGMA.2008.018