The p-norm joint spectral radius is defined by a bounded collection of square matrices with complex entries and of the same size. In the present paper the author investigates the p-norm joint spectral radius for integ...The p-norm joint spectral radius is defined by a bounded collection of square matrices with complex entries and of the same size. In the present paper the author investigates the p-norm joint spectral radius for integers. The method introduced in this paper yields some basic formulas for these spectral radii. The approach used in this paper provides a simple proof of Berger-Wang' s relation concerning the ∞-norm joint spectral radius.展开更多
A soliton hierarchy of multicomponent AKNS equations is generated from an arbitraryorder matrix spectral problem, along with its bi-Hamiltonian formulation. Adjoint symmetry constraints are presented to manipulate bi...A soliton hierarchy of multicomponent AKNS equations is generated from an arbitraryorder matrix spectral problem, along with its bi-Hamiltonian formulation. Adjoint symmetry constraints are presented to manipulate binary nonlinearization for the associated arbitrary order matrix spectral problem. The resulting spatial and temporal constrained flows are shown to provide integrable decompositions of the multicomponent AKNS equations.展开更多
A new approach to construct a new 4×4 matrix spectral problem from a normal 2×2 matrix spectral problem is presented.AKNS spectral problem is discussed as an example.The isospectral evolution equation of the...A new approach to construct a new 4×4 matrix spectral problem from a normal 2×2 matrix spectral problem is presented.AKNS spectral problem is discussed as an example.The isospectral evolution equation of the new 4×4 matrix spectral problem is nothing but the famous AKNS equation hierarchy.With the aid of the binary nonlino earization method,the authors get new integrable decompositions of the AKNS equation. In this process,the r-matrix is used to get the result.展开更多
文摘The p-norm joint spectral radius is defined by a bounded collection of square matrices with complex entries and of the same size. In the present paper the author investigates the p-norm joint spectral radius for integers. The method introduced in this paper yields some basic formulas for these spectral radii. The approach used in this paper provides a simple proof of Berger-Wang' s relation concerning the ∞-norm joint spectral radius.
基金Research Grants Council of Hong Kong(CERG 9040466)City University of Hong Kong(SRGs 7001041,7001178)+2 种基金National Science Foundation of China(No.19801031)Special Grant of Excellent PhD Thesis(No.200013)Special Funds for Major State Basjc Reaca
文摘A soliton hierarchy of multicomponent AKNS equations is generated from an arbitraryorder matrix spectral problem, along with its bi-Hamiltonian formulation. Adjoint symmetry constraints are presented to manipulate binary nonlinearization for the associated arbitrary order matrix spectral problem. The resulting spatial and temporal constrained flows are shown to provide integrable decompositions of the multicomponent AKNS equations.
基金the National Natural Science Foundation of China(No.10671121).
文摘A new approach to construct a new 4×4 matrix spectral problem from a normal 2×2 matrix spectral problem is presented.AKNS spectral problem is discussed as an example.The isospectral evolution equation of the new 4×4 matrix spectral problem is nothing but the famous AKNS equation hierarchy.With the aid of the binary nonlino earization method,the authors get new integrable decompositions of the AKNS equation. In this process,the r-matrix is used to get the result.
