96-165 F. Gesztesy and R. Ratnaseelan

An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy (115K, amslatex 1.2) May 2, 96

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Abstract. We develop an alternative systematic approach to the AKNS hierarchy based on elementary algebraic methods. In particular, we recursively construct Lax pairs for the entire AKNS hierarchy by introducing a fundamental polynomial formalism and establish the basic algebro-geometric setting including associated Burchnall-Chaundy curves, Baker-Akhiezer functions, trace formulas, Dubrovin-type equations for analogs of Dirichlet and Neumann divisors, and theta function representations for algebro-geometric solutions.

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