A C. Neumann system is presented in this paper. This system is generated through the nonlinearization of the Levi spectral problem under the so-called C. Neumann constraint. We prove that the C. Neumann system is comp...A C. Neumann system is presented in this paper. This system is generated through the nonlinearization of the Levi spectral problem under the so-called C. Neumann constraint. We prove that the C. Neumann system is completely integrable in the Liouville sense. The involutive solutions of the Levi hierarchy are given. Particularly, on the tangent bundle of the sphere SN-1. theinvolutive solutions of the well-known Burgers equation ut=uxx-2uux and MKdV equation ut=-uxxx+6u2ux are obtained.展开更多
The conservation laws of the Levi equation are presented.Two types of symmetry of the Levi equationhierarchy are deduced.Further it is proved that these symmetries construct an infinite-dimensional Lie algebra.
文摘A C. Neumann system is presented in this paper. This system is generated through the nonlinearization of the Levi spectral problem under the so-called C. Neumann constraint. We prove that the C. Neumann system is completely integrable in the Liouville sense. The involutive solutions of the Levi hierarchy are given. Particularly, on the tangent bundle of the sphere SN-1. theinvolutive solutions of the well-known Burgers equation ut=uxx-2uux and MKdV equation ut=-uxxx+6u2ux are obtained.
基金National Natural Science Foundation of China under Grant Nos.10871165 and 10671121
文摘The conservation laws of the Levi equation are presented.Two types of symmetry of the Levi equationhierarchy are deduced.Further it is proved that these symmetries construct an infinite-dimensional Lie algebra.
基金Supported by National Natural Science Foundation of China(10971220)the FANEDD(200919)+1 种基金the Fundamental Research Funds for the Central UniversitiesYouth Foundation of China University of Mining and Technology(2007A029)
