Integrable Systems with Unitary Invariance from Non-stretching Geometric   Curve Flows in the Hermitian Symmetric Space Sp(n)/U(n)
  A moving parallel frame method is applied to geometric non-stretching curve flows in the Hermitian symmetric space Sp(n)/U(n) to derive new integrable systems with unitary invariance. These systems consist of a bi-Hamiltonian modified Korteweg-de Vries equation and a Hamiltonian sine-Gordon (SG) equation, involving a scalar variable coupled to a complex vector variable. The Hermitian structure of the symmetric space Sp(n)/U(n) is used in a natural way from the beginning in formulating a complex matrix representation of the tangent space sp(n)/u(n) and its bracket relations within the symmetric Lie algebra (u(n),sp(n)). 
Stephen C. Anco, Esmaeel Asadi, Asieh Dogonchi
nlin.SI math-ph math.MP