## Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach.(English)Zbl 0909.34073

Summary: The authors provide an overview on elliptic algebro-geometric solutions of the KdV and AKNS hierarchies, with special emphasis on Floquet theoretic and spectral theoretic methods. The treatment includes an effective characterization of all stationary elliptic KdV and AKNS solutions based on a theory developed by Hermite and Picard.

### MSC:

 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 35Q53 KdV equations (Korteweg-de Vries equations) 35Q55 NLS equations (nonlinear Schrödinger equations) 34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) 34L05 General spectral theory of ordinary differential operators 35Q51 Soliton equations
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### References:

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