No abstract

No abstract

No abstract

a b s t r a c tWith the help of the Lax matrix, the Hu hierarchy is decomposed into two systems of solvable ordinary differential equations. Based on the theory of algebraic curves, the Abel-Jacobi coordinates are introduced to straighten out all the flows related to the entire hierarchy. Algebro-geometric solutions for the entire Hu hierarchy are obtained by using asymptotic expansion of the meromorphic function and its Riemann theta function representation.

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.