The Veselov's discrete Neumann system is derived through nonlinearization of a discrete spectral problem.Based on the commutative relation between the Lax matrix and the Darboux matrix with finite genus potentials...The Veselov's discrete Neumann system is derived through nonlinearization of a discrete spectral problem.Based on the commutative relation between the Lax matrix and the Darboux matrix with finite genus potentials,a special solution is calculated with the help of the Baker-Akhiezer-Kriechever function.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
基金Supported by the National Natural Science Foundation of China under Grant No. 10971200
文摘The Veselov's discrete Neumann system is derived through nonlinearization of a discrete spectral problem.Based on the commutative relation between the Lax matrix and the Darboux matrix with finite genus potentials,a special solution is calculated with the help of the Baker-Akhiezer-Kriechever function.
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.
