Why the general Zakharov-Shabat equations form a hierarchy?

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.

13pp

References in corpus (2)

• Additional symmetries of KP, Grassmannian, and the string equation
• Moment Maps to Loop Algebras, Classical R-Matrix and Integrable Systems