On canonical coordinates in soliton hierarchies

Canonical coordinates of the type (L,M) or (L,G), $G = WxW^{-1}$, are considered in connection with semiclassical or dispersionless limits $(\lambda,\mathcal M)$ or $(\lambda,\hat \xi)$. Connections of soliton hierarchies to Hamilton–Jacobi theory for dKP and to action principles and gravity for KdV are indicated.