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
The Rosochatius system on the sphere, an integrable mechanical system discovered in the nineteenth century, is investigated in a suitably chosen framework with the sphere as an invariant set, to avoid the complicated ...The Rosochatius system on the sphere, an integrable mechanical system discovered in the nineteenth century, is investigated in a suitably chosen framework with the sphere as an invariant set, to avoid the complicated constraint presentations. Higher order Rosochatius flows are defined and straightened out in the Jacobi variety of the associated hyperelliptic curve. A relation is found between these flows and the KdV equation, whose finite genus solution is calculated in the context of the Rosoehatius hierarchy.展开更多
We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-c...We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-consistent sources and its Lax representation are presented.展开更多
A Bcklund transformation of the restricted mKdV flow with a Rosochatius deformation is constructed.Its Lax representation and thus N invariants in involution are presented.Such Bcklund transformation is a Rosochatius ...A Bcklund transformation of the restricted mKdV flow with a Rosochatius deformation is constructed.Its Lax representation and thus N invariants in involution are presented.Such Bcklund transformation is a Rosochatius deformation of that of the restricted mKdV flow.展开更多
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.
基金Supported by the National Natural Science Foundation of China under Grant No.10971200
文摘The Rosochatius system on the sphere, an integrable mechanical system discovered in the nineteenth century, is investigated in a suitably chosen framework with the sphere as an invariant set, to avoid the complicated constraint presentations. Higher order Rosochatius flows are defined and straightened out in the Jacobi variety of the associated hyperelliptic curve. A relation is found between these flows and the KdV equation, whose finite genus solution is calculated in the context of the Rosoehatius hierarchy.
基金Supported by the Research Work of Liaoning Provincial Development of Education under Grant No.L2010513
文摘We propose a method to construct the integrable Rosochatius deformations for an integrable couplingsequations hierarchy.As applications, the integrable Rosochatius deformations of the coupled CKdV hierarchy withself-consistent sources and its Lax representation are presented.
基金Supported by the National Natural Science Foundation of China under Grant No.11271168
文摘A Bcklund transformation of the restricted mKdV flow with a Rosochatius deformation is constructed.Its Lax representation and thus N invariants in involution are presented.Such Bcklund transformation is a Rosochatius deformation of that of the restricted mKdV flow.
