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An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy

Fritz Gesztesy·Ratnam Ratnaseelan
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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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Fritz Gesztesy, Ratnam Ratnaseelan. 1997-07-14. An Alternative Approach to Algebro-Geometric Solutions of the AKNS Hierarchy. https://doi.org/10.1142/s0129055x98000112

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