Why the general Zakharov-Shabat equations form a hierarchy?

Details Why the general Zakharov-Shabat equations form a hierarchy? Why the general Zakharov-Shabat equations form a hierarchy?

1993-05-21

arxiv.org/abs/hep-th/9305108v1

Commun. Math. Phys. 163 (1994) 509-522

Physics

High Energy Physics

High Energy Physics - Theory

13pp

Scientific paper

10.1007/BF02101461

The totality of all Zakharov-Shabat equations (ZS), i.e., zero-curvature equations with rational dependence on a spectral parameter, if properly defined, can be considered as a hierarchy. The latter means a collection of commuting vector fields in the same phase space. Further properties of the hierarchy are discussed, such as additional symmetries, an analogue to the string equation, a Grassmannian related to the ZS hierarchy, and a Grassmannian definition of soliton solutions.

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