Treibich-Verdier potentials and the stationary (m)KdV hierarchy. (English) Zbl 0830.35119
Summary: The elliptic finite-gap solutions of the stationary Korteweg-de Vries (KdV) hierarchy recently introduced by Treibich and Verdier are analyzed in detail on the basis of a theorem due to Picard. Analogous results are derived for the first time in the context of the stationary modified Korteweg-de Vries (mKdV) hierarchy. Our approach extends to general elliptic finite-gap solutions of the (m)KdV hierarchy.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 14H52 | Elliptic curves |
Keywords:
Picard potential; Weierstraß function; KdV hierarchy; mKdV hierarchy; elliptic finite-gap solutionsReferences:
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