Hamiltonian Flows of Curves in G / SO ( N ) and Vector Soliton Equations of mKdV and Sine-Gordon Type

@inproceedings{Anco2006HamiltonianFO,
  title={Hamiltonian Flows of Curves in G / SO ( N ) and Vector Soliton Equations of mKdV and Sine-Gordon Type},
  author={Stephen C. Anco},
  year={2006}
}
The bi-Hamiltonian structure of the two known vector generalizations of the mKdV hierarchy of soliton equations is derived in a geometrical fashion from flows of nonstretching curves in Riemannian symmetric spaces G/SO(N). These spaces are exhausted by the Lie groups G = SO(N + 1), SU(N). The derivation of the bi-Hamiltonian structure uses a parallel frame and connection along the curve, tied to a zero curvature Maurer–Cartan form on G, and this yields the mKdV recursion operators in a… CONTINUE READING
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