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.
In this paper, a new completely integrable system related to the complex spectral problem -φ xx＋（i/4）wpx＋（i/4）（wp）x＋（1/4）vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. According to the viewpoint of Hamiltonian mechanics, the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the constrained conditions between the potentiaJ u, v and the eigenfunction φ, the involutive representations of the solutions for the Boussinesq equation hieraxchy axe given.
