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 |
Keywords:
elliptic algebro-geometric solutions; KdV and AKNS hierarchies; Floquet theoretic and spectral theoretic methods; stationary elliptic KdV and AKNS solutionsReferences:
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