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

Luen Chau Li, Irina Nenciu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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