Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable coup...Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.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
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
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
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 those...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
基金supported by the National Natural Science Foundation of China(1127100861072147+1 种基金11071159)the First-Class Discipline of Universities in Shanghai and the Shanghai University Leading Academic Discipline Project(A13-0101-12-004)
文摘Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.
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.
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.
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 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.
