On the zeros of the KdV soliton Baker–Akhiezer function

Recent results concerning the zeros of the KdV soliton Baker–Akhiezer function are outlined. Specifically, it is shown that the zeros of the wave function of a one-dimensional Schrodinger operator with a reflectionless potential are characterized by (i) the equations of motion of a rational Ruijsenaars–Schneider particle system with harmonic term and (ii) a nonlinear algebraic system of Bethe-type equations. The integration of the particle system provides us with an explicit parametrization of the solution curve of the Bethe equations. The flows corresponding to the higher integrals of the particle system encode the dynamics of the zeros of the solitonic Baker–Akhiezer function for the KdV hierarchy.