Reduction of bihamiltonian systems and separation of variables: an example from the Boussinesq hierarchy
Abstract
We discuss the Boussinesq system with
t
5
stationary, within a general framework for the analysis of stationary flows of n-Gel'fand-Dickey hierarchies. We show how a careful use of its bihamiltonian structure can be used to provide a set of separation coordinates for the corresponding Hamilton--Jacobi equations.