Straightening out of the flows for the Hu hierarchy and its algebro-geometric solutions

With 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.