Stephen C Anco and Esmaeel Asadi 2009 J. Phys. A: Math. Theor. 42 485201 doi:10.1088/1751-8113/42/48/485201
Quaternionic soliton equations from Hamiltonian curve flows in 
Stephen C Anco and Esmaeel Asadi
Show affiliationsA 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 M = G/H 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 Korteweg-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 Schrödinger map.
- PACS
- MSC
-
37K40 Soliton theory, asymptotic behavior of solutions
35Q55 NLS-like (nonlinear Schrödinger) equations (See also 37K10)
- Subjects
- Dates
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Issue 48 (4 December 2009)
Received 26 May 2009, in final form 7 October 2009
Published 11 November 2009
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Quaternionic soliton equations from Hamiltonian curve flows in
Stephen C Anco and Esmaeel Asadi 2009 J. Phys. A: Math. Theor. 42 485201
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