Integrable systems with unitary invariance from non-stretching geometric curve flows in the Hermitian symmetric space Sp (n)/U (n)
International Journal of Modern Physics: Conference Series, 2015•World Scientific
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 …
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 …
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)).
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