On commuting differential operators of rank 2 corresponding to trigonal spectral curves of genus 3

The construction of ordinary commuting differential operators is a classical problem of differential equations and integrable systems, which has applications to soliton theory. Commuting operators of rank 1 were found by Krichever. The problem of constructing operators of rank l>1 has not been solved in the general case. In all known examples of operators of rank l>1, the spectral curves are hyperelliptic curves. In this paper, the first examples of operators of rank 2, corresponding to trigonal spectral curves of genus 3, are constructed.