Algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy

This paper is dedicated to provide explicit theta function representation of algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy. Our main tools include zero-curvature equation to derive the generalized nonlinear Schrödinger hierarchy, the hyper-elliptic curve with genus of N, the Abel-Jacobi coordinates, the meromorphic function, the Baker-Akhiezer functions, and the Dubrovin-type equations for auxiliary divisors. With the help of these tools, the explicit representations of the Baker-Ahhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the whole generalized nonlinear Schrödinger hierarchy.