A new discrete isospectral problem is introduced,from which the coupled discrete KdV hierarchy is deduced and is written in its Hamiltonian form by means of the trace identity.It is shown that each equation in the res...A new discrete isospectral problem is introduced,from which the coupled discrete KdV hierarchy is deduced and is written in its Hamiltonian form by means of the trace identity.It is shown that each equation in the resulting hierarchy is Liouville integrable.Furthermore,an infinite number of conservation laws are shown explicitly by direct computation.展开更多
A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. T...A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. The corresponding reductions and the exact solutions due to the methods of the ordinary differential equations are then given by the methods. The results given here answer partially an open problem proposed by Clarkson, that is how to develop the direct method to seek symmetry reductions of nonlinear PDEs with arbitrary functions.展开更多
In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke compari...In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen’s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed. MR Subject Classification 34C25 - 92D25 Keywords ecological invasion - diffusion - permanence - predation global stability Supported by the Research Foundation of Education Department of Zhejiang Province (20038049).展开更多
A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable sym...A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonli-nearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resulting lattice soliton equations.展开更多
基金Scientific Research Award Foundation for Shandong Provincial outstanding young andmiddle- aged scientist
文摘A new discrete isospectral problem is introduced,from which the coupled discrete KdV hierarchy is deduced and is written in its Hamiltonian form by means of the trace identity.It is shown that each equation in the resulting hierarchy is Liouville integrable.Furthermore,an infinite number of conservation laws are shown explicitly by direct computation.
基金the National Natural Science Foundation of China(1 990 1 0 2 7)
文摘A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. The corresponding reductions and the exact solutions due to the methods of the ordinary differential equations are then given by the methods. The results given here answer partially an open problem proposed by Clarkson, that is how to develop the direct method to seek symmetry reductions of nonlinear PDEs with arbitrary functions.
基金Supported by the Research Foundation of Education Department of Zhejiang Province( 2 0 0 380 4 9)
文摘In this paper, an important problem arising from conservation biology is considered. Namely, how does the introduced species affect the survival of a native endangered species through predation? By using Kamke comparison theorem and some results in Cui and Chen’s paper (1998), some sufficient conditions that guarantee the permanence of the species and global stability of a unique positive periodic solution are obtained. Biological implication of these results are discussed. MR Subject Classification 34C25 - 92D25 Keywords ecological invasion - diffusion - permanence - predation global stability Supported by the Research Foundation of Education Department of Zhejiang Province (20038049).
文摘A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonli-nearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resulting lattice soliton equations.
