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Complete Integrability of Completely Integrable Systems

R. Beals·D. H. Sattinger
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Abstract

The question of complete integrability of evolution equations associated to $n\times n$ first order isospectral operators is investigated using the inverse scattering method. It is shown that for $n>2$, 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 groups GL(n) and SU(n).}

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R. Beals, D. H. Sattinger. 1997-12-15. Complete Integrability of Completely Integrable Systems. https://doi.org/10.1007/bf02102035

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