3 research outputs found
Quaternionic Soliton Equations from Hamiltonian Curve Flows in HP^n
A bi-Hamiltonian hierarchy of quaternion soliton equations is derived from
geometric non-stretching flows of curves in the quaternionic projective space
. The derivation adapts the method and results in recent work by one of
us on the Hamiltonian structure of non-stretching curve flows in Riemannian
symmetric spaces by viewing as a
symmetric space in terms of compact real symplectic groups and quaternion
unitary groups. As main results, scalar-vector (multi-component) versions of
the sine-Gordon (SG) equation and the modified Korteveg-de Vries (mKdV)
equation are obtained along with their bi-Hamiltonian integrability structure
consisting of a shared hierarchy of quaternionic symmetries and conservation
laws generated by a hereditary recursion operator. The corresponding geometric
curve flows in are shown to be described by a non-stretching wave map
and a mKdV analog of a non-stretching Schrodinger map.Comment: 25 pages; typos correcte