Commuting differential operators of rank 2 with rational coefficients
  In this paper we find new self-adjoint commuting operators of rank 2 with rational coefficients and prove that any elliptic and hyperelliptic curves of genus 2 are spectral curves of commuting operators with rational coefficients. Also the case when curves of genus 3 are spectral curves of commuting operators with rational coefficients is studied. 
Vardan Oganesyan
nlin.SI math-ph math.AG math.CA math.MP