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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
Article

Abstract

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).

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Evolution Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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