Communications in Mathematical Physics

, Volume 138, Issue 3, pp 409–436 | Cite as

On the complete integrability of completely integrable systems

  • Richard Beals
  • D. H. Sattinger


The question of complete integrability of evolution equations associated ton×n first order isospectral operators is investigated using the inverse scattering method. It is shown that forn>2, e.g. for the three-wave interaction, additional (nonlinear) pointwise flows are necessary for the assertion of complete integrability. Their existence is demonstrated by constructing action-angle variables. This construction depends on the analysis of a natural 2-form and symplectic foliation for the groupsGL(n) andSU(n).


Neural Network Statistical Physic Complex System Nonlinear Dynamics Evolution Equation 
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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Richard Beals
    • 1
  • D. H. Sattinger
    • 2
  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.School of MathematicsUniversity of MinnesotaMinneapolisUSA

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