AN ALTERNATIVE APPROACH TO ALGEBRO-GEOMETRIC SOLUTIONS OF THE AKNS HIERARCHY

We develop an alternative systematic approach to the AKNS hierarchy ba sed on elementary algebraic methods. In particular, we recursively con struct Lax pairs for the entire AKNS hierarchy by introducing a fundam ental polynomial formalism and establish the basic algebro-geometric s etting including associated Burchnall-Chaundy curves, Baker-Akhiezer f unctions, trace formulas, Dubrovin-type equations for analogs of Diric hlet and Neumann divisors, and theta function representations for alge bro-geometric solutions.