On Moments of Negative Eigenvalues of an Elliptic Operator

A new method of constructing elliptic finite-gap solutions of the stationary Korteweg-de Vries (KdV) hierarchy, based on a theorem due to PICARD , is illustrated in the concrete case of the Lamé-Ince potentials -s(s + 1) ρ(z), sε (ρ(.) the elliptic Weierstrass function). Analogous results are derived in the context of the stationary modified Korteweg-de Vries (mKd V) hierarchy for the first time.