The coupled Sasa–Satsuma hierarchy: Trigonal curve and finite genus solutions

Abstract

Based on the Lenard recursion equations and the stationary zero-curvature equation, we derive the coupled Sasa–Satsuma hierarchy, in which a typical number is the coupled Sasa–Satsuma equation. The properties of the associated trigonal curve and the meromorphic functions are studied, which naturally give the essential singularities and divisors of the meromorphic functions. By comparing the asymptotic expansions for the Baker–Akhiezer function and its Riemann theta function representation, we arrive at the finite genus solutions of the whole coupled Sasa–Satsuma hierarchy in terms of the Riemann theta function.