This article is cited in 3 papers

Integrable vector evolution equations admitting zeroth-order conserved densities

M. Yu. Balakhnev, A. G. Meshkov

Orel State University for Technology, Orel, Russia

Abstract: In the symmetry approach framework, we solve the problem of classifying third-order integrable vector evolution equations that have zeroth-order conserved densities. We obtain the complete list of nine equations of this form. Two equations in the list were previously unknown. We find auto-Bäcklund transformations for the new equations.

Keywords: canonical density, integrable evolution equation, Bäcklund transformation.

Received: 27.10.2009

DOI: 10.4213/tmf6534

 English version: Theoretical and Mathematical Physics, 2010, 164:2, 1002–1007

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