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Schrödinger flows, binormal motion for curves and the second AKNS-hierarchies. (English) Zbl 1048.37058
Summary: We present a unified geometric interpretation of the second AKNS-hierarchies via the geometric concept of Schrödinger flows in the category of symplectic manifolds and binormal motion for curves in the Minkowski 3-space.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
37K25 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry
53C55 Global differential geometry of Hermitian and Kählerian manifolds
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