@article{a09d7a27a773429c919b911b34335439,

title = "The periodic defocusing Ablowitz-Ladik equation and the geometry of Floquet CMV matrices",

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.",

author = "Li, {Luen Chau} and Irina Nenciu",

note = "Funding Information: The first author would like to thank Jiang-Hua Lu for reminding him of the Bruhat Poisson structure during a visit to the University of Hong Kong. He is also grateful to MSRI and the organizers of the Program on Random matrices, Interacting Particle Systems and Integrable Systems for the hospitality during his stay in Berkeley in the Fall of 2010 where part of this work was being done. The second author would like to acknowledge the support of NSF grant DMS-0701026 . Finally, the authors thank Barry Simon and Percy Deift for their advice to include a summary of the main theorems in the introductory section. ",

year = "2012",

month = dec,

day = "20",

doi = "10.1016/j.aim.2012.08.006",

language = "English (US)",

volume = "231",

pages = "3330--3388",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

number = "6",

}