### 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 language | English (US) |
---|---|

Pages (from-to) | 3330-3388 |

Number of pages | 59 |

Journal | Advances in Mathematics |

Volume | 231 |

Issue number | 6 |

DOIs | |

State | Published - Dec 20 2012 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

*Advances in Mathematics*,

*231*(6), 3330-3388. https://doi.org/10.1016/j.aim.2012.08.006

}

*Advances in Mathematics*, vol. 231, no. 6, pp. 3330-3388. https://doi.org/10.1016/j.aim.2012.08.006

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - The periodic defocusing Ablowitz-Ladik equation and the geometry of Floquet CMV matrices

AU - Li, Luen Chau

AU - Nenciu, Irina

PY - 2012/12/20

Y1 - 2012/12/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84867137806&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867137806&partnerID=8YFLogxK

U2 - 10.1016/j.aim.2012.08.006

DO - 10.1016/j.aim.2012.08.006

M3 - Article

AN - SCOPUS:84867137806

VL - 231

SP - 3330

EP - 3388

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

IS - 6

ER -