An algebraic characterization of the Korteweg-de Vries hierarchy

摘要

The conserved polynomials of the Korteweg-de Vries equation u(t) = u(xxx) - 12uu(x) are characterized by the vanishing of the residues of their associated differential polynomials evaluated on the formal power series of the kind u = x(-2) + u(0) + Sigma (n greater than or equal to2)u(n)x(n). [References: 12]