Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4666293 | Advances in Mathematics | 2012 | 59 Pages |
Abstract
In this work, we show that the periodic defocusing Ablowitz-Ladik equation can be expressed as an isospectral deformation of Floquet CMV matrices. We then introduce a Poisson Lie group whose underlying group is a loop group and show that the set of Floquet CMV matrices is a Coxeter dressing orbit of this Poisson Lie group. By using the group-theoretic framework, we establish the Liouville integrability of the equation by constructing action-angle variables, we also solve the Hamiltonian equations generated by the commuting flows via Riemann-Hilbert factorization problems.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Luen-Chau Li, Irina Nenciu,