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Integrable vector evolution equations admitting zeroth-order conserved densities

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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.

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Authors and Affiliations

  1. Orel State University for Technology, Orel, Russia

    M. Yu. Balakhnev & A. G. Meshkov

Authors
  1. M. Yu. Balakhnev
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  2. A. G. Meshkov
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Correspondence to M. Yu. Balakhnev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 164, No. 2, pp. 207–213, August, 2010.

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Balakhnev, M.Y., Meshkov, A.G. Integrable vector evolution equations admitting zeroth-order conserved densities. Theor Math Phys 164, 1002–1007 (2010). https://doi.org/10.1007/s11232-010-0080-9

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  • DOI: https://doi.org/10.1007/s11232-010-0080-9

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