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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:1410.1230 (nlin)
[Submitted on 6 Oct 2014]

Title:Integrable Systems with Unitary Invariance from Non-stretching Geometric Curve Flows in the Hermitian Symmetric Space Sp(n)/U(n)

Authors:Stephen C. Anco, Esmaeel Asadi, Asieh Dogonchi
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Abstract: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)).
Comments: 14 pages
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph)
Cite as: arXiv:1410.1230 [nlin.SI]
  (or arXiv:1410.1230v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.1410.1230
Journal reference: Int. J. Modern Phys. 38 (2015), 1560071 (15 pages)
Related DOI: https://doi.org/10.1142/S201019451560071X

Submission history

From: Stephen C. Anco [view email]
[v1] Mon, 6 Oct 2014 00:37:51 UTC (14 KB)
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