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
Bosonization approach is applied in solving the most general ;N= 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a （sKdV-a） equation. By introducing some fermionic parameters in the expansion...Bosonization approach is applied in solving the most general ;N= 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a （sKdV-a） equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosoNic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonie equations are simply obtained for all values of a, Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.展开更多
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 National Natural Science Foundation of China under Nos.11175092,11275123 and 10905038Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201017148K.C.Wong Magna Fund in Ningbo University
文摘Bosonization approach is applied in solving the most general ;N= 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a （sKdV-a） equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosoNic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonie equations are simply obtained for all values of a, Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.
