The dynamics of zeros of the elliptic solutions to the Schrodinger equation

TL;DR

This paper generalizes the understanding of how zeros of elliptic solutions to the Schrödinger equation evolve over time, extending previous results from the solitonic case to elliptic potentials using algebraic-geometrical methods.

Contribution

It introduces a novel algebraic-geometrical approach to describe the dynamics of zeros in elliptic solutions, broadening the scope beyond the rational case.

Findings

Zeros' dynamics governed by elliptic Ruijsenaars-Schneider system

Extension from rational to elliptic potentials

Use of algebraic-geometrical construction for solutions

Abstract

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.