Abstract:
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.
Fulltext:
PDF file (496 kB)