Hamiltonian Flows of Curves in symmetric spaces G/SO(N) and Vector Soliton Equations of mKdV and Sine-Gordon Type
Anco, Stephen C.
arXiv, 0512046 / Harvested from arXiv
Text on arXiv
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 non-stretching 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 curves, tied to a zero curvature Maurer-Cartan form on G, and this yields the vector mKdV recursion operators in a geometric O(N-1)-invariant form. The kernel of these recursion operators is shown to yield two hyperbolic vector generalizations of the sine-Gordon equation. The corresponding geometric curve flows in the hierarchies are described in an explicit form, given by wave map equations and mKdV analogs of Schrodinger map equations.
Publié le : 2005-12-19
Classification:  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  Mathematical Physics,  Mathematics - Analysis of PDEs 
@article{0512046,
     author = {Anco, Stephen C.},
     title = {Hamiltonian Flows of Curves in symmetric spaces G/SO(N) and Vector
  Soliton Equations of mKdV and Sine-Gordon Type},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0512046}
}

Anco, Stephen C. Hamiltonian Flows of Curves in symmetric spaces G/SO(N) and Vector
  Soliton Equations of mKdV and Sine-Gordon Type. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0512046/