Hill's Spectral Curves and the Invariant Measure of the Periodic KdV Equation

Gordon Blower, Caroline Brett, Ian Doust

This paper analyses the periodic spectrum of Schrödinger's equation $-f^{\prime \prime }+qf=\lambda f$ when the potential is real, periodic, random and subject to the invariant measure ${\nu }_N^{\beta }$ of the pe…