The dynamics of zeros of the elliptic solutions to the Schrodinger   equation
  J. F. van Diejen and H. Puschmann have recently shown that the dynamics of zeros of the n-solitonic solutions to the Schrodinger equation with the reflectionless potential is governed by a rational Ruijsenaars-Schneider system. We use the algebraic-geometrical construction of solutions to the Schrodinger equation to generalize this result to the elliptic case. 
A. Akhmetshin, Y. Volvovsky