完全可积系统的完全可积性
Complete Integrability of Completely Integrable Systems
摘要：
利用逆散射方法研究了与$n\times n$一阶等谱算子相关的发展方程的完全可积性问题。结果表明，对于$n>2$，例如三波相互作用，额外的（非线性）逐点流是必要的断言完全可积性。通过构造作用角变量证明了它们的存在。这种构造依赖于对群GL（n）和SU（n）的自然2-形式和辛叶理的分析。
英文摘要：
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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