A Finite-Dimensional Completely Integrable System Associated with Boussinesq Hierarchy

摘要

In this paper,a new completely integrable system related to the complex spectral problem —φ_(xx)+(i/4)uφ_x+(i/4)(uφ)_x+(1/4)vφ=iλφ_x and the constrained Bows of the Boussinesq equations are generated.According to theviewpoint of Hamiltonian mechanics,the Euler-Lagrange equations and the Legendre transformations,a reasonableJacobi-Ostrogradsky coordinate system is obtained.Moreover,by means of the constrained conditions between thepotential u,v and the eigenfunction φ,the involutive representations of the solutions for the Boussinesq equationhierarchy are given.