On the complete integrability of some lax equations on a periodic lattice

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We consider some Lax equations on a periodic lattice with N = 2 sites under which the monodromy matrix evolves according to the Toda flows. To establish their integrability (in the sense of Liouville) on generic symplectic leaves of the underlying Poisson structure, we construct the action-angle variables explicitly. The action variables are invariants of certain group actions. In particular, one collection of these invariants is associated with a spectral curve and the linearization of the associated Hamilton equations involves interesting new feature. We also prove the injectivity of the linearization map into real variables and solve the Hamilton equations generated by the invariants via factorization problems.

Original languageEnglish (US)
Pages (from-to)331-372
Number of pages42
JournalTransactions of the American Mathematical Society
Volume349
Issue number1
StatePublished - 1997

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Lax Equation
Complete Integrability
Linearization
Real variables
Invariant
Factorization
Action-angle Variables
Spectral Curve
Poisson Structure
Injectivity
Monodromy
Group Action
Integrability
Leaves

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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On the complete integrability of some lax equations on a periodic lattice. / Li, Luen-chau.

In: Transactions of the American Mathematical Society, Vol. 349, No. 1, 1997, p. 331-372.

Research output: Contribution to journalArticle

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