Geodesic
Integrable vector evolution equations admitting zeroth-order conserved densities
Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 207-213

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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. 
@article{TMF_2010_164_2_a2,
     author = {M. Yu. Balakhnev and A. G. Meshkov},
     title = {Integrable vector evolution equations admitting zeroth-order conserved densities},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {207--213},
     publisher = {mathdoc},
     volume = {164},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a2/}
}
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M. Yu. Balakhnev; A. G. Meshkov. Integrable vector evolution equations admitting zeroth-order conserved densities. Teoretičeskaâ i matematičeskaâ fizika, Tome 164 (2010) no. 2, pp. 207-213. http://geodesic.mathdoc.fr/item/TMF_2010_164_2_a2/