The periodic defocusing Ablowitz-Ladik equation and the geometry of Floquet CMV matrices

Luen Chau Li, Irina Nenciu

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)3330-3388
Number of pages59
JournalAdvances in Mathematics
Volume231
Issue number6
DOIs
StatePublished - Dec 20 2012

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Poisson-Lie Groups
Action-angle Variables
Loop Groups
Hilbert
Integrability
Factorization
Orbit
Framework

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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The periodic defocusing Ablowitz-Ladik equation and the geometry of Floquet CMV matrices. / Li, Luen Chau; Nenciu, Irina.

In: Advances in Mathematics, Vol. 231, No. 6, 20.12.2012, p. 3330-3388.

Research output: Contribution to journalArticle

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