An isospectral problem with four potentials is discussed. The corresponding hierarchy of nonlinearevolution equations is derived. It is shown that the AKNS, Levi, D-AKNS hierarchies and a new oneare reductions of the... An isospectral problem with four potentials is discussed. The corresponding hierarchy of nonlinearevolution equations is derived. It is shown that the AKNS, Levi, D-AKNS hierarchies and a new oneare reductions of the above hierarchy. In each case the relevant Hamiltonian form is established bymaking use of the trase identity.展开更多
An isospectral problem with four potentials is discussed. The corresponding hierarchy of Lax integrable evolution equations is derived. For the hierarchy, it is shown that there exist other new reductions except thos... An isospectral problem with four potentials is discussed. The corresponding hierarchy of Lax integrable evolution equations is derived. For the hierarchy, it is shown that there exist other new reductions except those presented by Tu, Meng and Ma. For each reduction case the relevant Hamiltonian structure is established by means of trace identity.展开更多
By introducing an invertible linear transform, a new Lie algebra G is obtained from the Lie algebra H. Making use of the compatibility conditions of the respective isospectral problems, a generalized NLS-MKdV hierarch...By introducing an invertible linear transform, a new Lie algebra G is obtained from the Lie algebra H. Making use of the compatibility conditions of the respective isospectral problems, a generalized NLS-MKdV hierarchy and a new integrable soliton hierarchy are achieved by using the trace identity or the variational identity. Then, two special non-semisimple Lie algebras ?and ?are explicitly conducted. As an application, the nonlinear continuous integrable couplings of the obtained integrable systems as well as their bi-Hamiltonian structures are established, respectively.展开更多
Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, it...Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.展开更多
A new discrete isospectral problem is introduced,from which a hierarchy of Lax i ntegrable lattice equation is deduced. By using the trace identity,the correspon ding Hamiltonian structure is given and its Liouville i...A new discrete isospectral problem is introduced,from which a hierarchy of Lax i ntegrable lattice equation is deduced. By using the trace identity,the correspon ding Hamiltonian structure is given and its Liouville integrability is proved.展开更多
Two isospectral-problems, that contain three potential u, v and w, are discussed. The corresponding hierarchies of nonlinear evolution equations are derived. It is shown that both the two hierarchies of equations shar...Two isospectral-problems, that contain three potential u, v and w, are discussed. The corresponding hierarchies of nonlinear evolution equations are derived. It is shown that both the two hierarchies of equations share a common interesting character that they admit a nonlinear reduction w=γ u v between the potentials with γ being a constant. In both the reduction cases the relevant Hamiltonian structures are established by using trace identity.展开更多
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
The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable sys- tems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by ...The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable sys- tems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by using the extended trace identity. As its application, we have obtained the Hamiltonian structures of the Yang hierarchy, the Korteweg-de-Vries （KdV） hierarchy, the multi-component Ablowitz-Kaup-Newell-Segur （M-AKNS） hierarchy, the multi-component Ablowitz-Kaup-Newell-Segur Kaup-Newell （M-AKNS-KN） hierarchy and a new multi-component integrable hierarchy separately.展开更多
基金The project supported by National Natural Science Foundation Committeethrough Nankai Institute of Mathematics
文摘 An isospectral problem with four potentials is discussed. The corresponding hierarchy of nonlinearevolution equations is derived. It is shown that the AKNS, Levi, D-AKNS hierarchies and a new oneare reductions of the above hierarchy. In each case the relevant Hamiltonian form is established bymaking use of the trase identity.
基金the Postdoctoral Science Foundation of China,Chinese National Basic Research Project "Mathematics Mechanization and a Platform for Automated Reasoning".
文摘 An isospectral problem with four potentials is discussed. The corresponding hierarchy of Lax integrable evolution equations is derived. For the hierarchy, it is shown that there exist other new reductions except those presented by Tu, Meng and Ma. For each reduction case the relevant Hamiltonian structure is established by means of trace identity.
文摘By introducing an invertible linear transform, a new Lie algebra G is obtained from the Lie algebra H. Making use of the compatibility conditions of the respective isospectral problems, a generalized NLS-MKdV hierarchy and a new integrable soliton hierarchy are achieved by using the trace identity or the variational identity. Then, two special non-semisimple Lie algebras ?and ?are explicitly conducted. As an application, the nonlinear continuous integrable couplings of the obtained integrable systems as well as their bi-Hamiltonian structures are established, respectively.
基金＊Supported by the Natural Science Foundation of China under Grant Nos. 61072147, 11071159, the Natural Science Foundation of Shanghai urlder Grant No. 09ZR1410800, the Shanghai Leading Academic Discipline Project under Grant No. J50101, and the National Key Basic Research Project of China under Grant No. KLMM0806
文摘Based on the basis of the constructed Lie super algebra, the super-isospectral problem of KN hierarchy is considered. Under the frame of the zero curvature equation, the super-KN hierarchy is obtained. Furthermore, its super-Hamiltonian structure is presented by using super-trace identity and it has super-bi-Hamiltonian structure.
文摘A new discrete isospectral problem is introduced,from which a hierarchy of Lax i ntegrable lattice equation is deduced. By using the trace identity,the correspon ding Hamiltonian structure is given and its Liouville integrability is proved.
文摘Two isospectral-problems, that contain three potential u, v and w, are discussed. The corresponding hierarchies of nonlinear evolution equations are derived. It is shown that both the two hierarchies of equations share a common interesting character that they admit a nonlinear reduction w=γ u v between the potentials with γ being a constant. In both the reduction cases the relevant Hamiltonian structures are established by using trace identity.
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Project supported by the National Natural Science Foundation of China （Grant Nos 10371070 and 10547123）. Acknowledgments The first author expresses her appreciation to the Soliton Research Team of Shanghai University, China for useful discussion.
文摘The trace identity is extended to the general loop algebra. The Hamiltonian structures of the integrable sys- tems concerning vector spectral problems and the multi-component integrable hierarchy can be worked out by using the extended trace identity. As its application, we have obtained the Hamiltonian structures of the Yang hierarchy, the Korteweg-de-Vries （KdV） hierarchy, the multi-component Ablowitz-Kaup-Newell-Segur （M-AKNS） hierarchy, the multi-component Ablowitz-Kaup-Newell-Segur Kaup-Newell （M-AKNS-KN） hierarchy and a new multi-component integrable hierarchy separately.
