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arXiv · hep-th/9305108

Why the general Zakharov-Shabat equations form a hierarchy?

L. A. Dickey
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Abstract

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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L. A. Dickey. 1993-05-21. Why the general Zakharov-Shabat equations form a hierarchy?. https://doi.org/10.1007/bf02101461

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