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 ...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.展开更多
Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy wi...Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy withself-consistent sources,of the TD hierarchy with self-consistent sources,and of the Jaulent Miodek hierarchy with self-consistentsources,together with their Lax representations are presented.展开更多
文摘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.
基金Supported by National Basic Research Program of China (973 Program) under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10801083
文摘Integrable Rosochatius deformations of finite-dimensional integrable systems are generalized to the solitonhierarchy with self-consistent sources.The integrable Rosochatius deformations of the Kaup-Newell hierarchy withself-consistent sources,of the TD hierarchy with self-consistent sources,and of the Jaulent Miodek hierarchy with self-consistentsources,together with their Lax representations are presented.
