Geodesic
Necessary integrability conditions for evolutionary lattice
Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 276-295

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We study the structure of solutions of the Lax equation $D_t(G)=[F,G]$ for formal series in powers of the shift operator. We show that if an equation with a given series $F$ of degree $m$ admits a solution $G$ of degree $k$, then it also admits a solution $H$ of degree $m$ such that $H^k=G^m$. We use this property to derive necessary integrability conditions for scalar evolutionary lattices.
Mots-clés : Volterra-type lattice
Keywords: higher symmetry, conservation law, integrability test. 
@article{TMF_2014_181_2_a2,
     author = {V. E. Adler},
     title = {Necessary integrability conditions for evolutionary lattice},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {276--295},
     publisher = {mathdoc},
     volume = {181},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a2/}
}
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V. E. Adler. Necessary integrability conditions for evolutionary lattice. Teoretičeskaâ i matematičeskaâ fizika, Tome 181 (2014) no. 2, pp. 276-295. http://geodesic.mathdoc.fr/item/TMF_2014_181_2_a2/