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
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 type of higher-dimensionaJ loop algebra is constructed from which an isospectral problem is established. It follows that an integrable coupling, actually an extended integrable model of the existed solitary hierarch...A type of higher-dimensionaJ loop algebra is constructed from which an isospectral problem is established. It follows that an integrable coupling, actually an extended integrable model of the existed solitary hierarchy of equations, is obtained by taking use of the zero curvature equation, whose Hamiltonian structure is worked out by employing the constructed quadratic identity.展开更多
By considering a new discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations of rational type are derived. It is shown that each equation in the resulting hierarchy is integrable in Liouville...By considering a new discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations of rational type are derived. It is shown that each equation in the resulting hierarchy is integrable in Liouville sense and possessing bi-Hamiltonian structure. Two types of semi-direct sums of Lie algebras are proposed, by using of which a practicable way to construct discrete integrable couplings is introduced. As applications, two kinds of discrete integrable couplings of the resulting system are worked out.展开更多
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
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
Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classic...Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classical-Boussinesq hierarchy is also integrable in the sense of Liouville.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
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
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.
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Supported by the Scientific Research Ability Foundation for Young Teacher of Northwest Normal University under Grant No.NWNULKQN -10-25
文摘A type of higher-dimensionaJ loop algebra is constructed from which an isospectral problem is established. It follows that an integrable coupling, actually an extended integrable model of the existed solitary hierarchy of equations, is obtained by taking use of the zero curvature equation, whose Hamiltonian structure is worked out by employing the constructed quadratic identity.
基金National Natural Science Foundation of China under Grant No.60572113the Natural Science Foundation of Shandong Province of China under Grant No.Q2006A04the Talents Foundation of Taishan College under Grant No.Y05-2-01
文摘By considering a new discrete isospectral eigenvalue problem, a hierarchy of lattice soliton equations of rational type are derived. It is shown that each equation in the resulting hierarchy is integrable in Liouville sense and possessing bi-Hamiltonian structure. Two types of semi-direct sums of Lie algebras are proposed, by using of which a practicable way to construct discrete integrable couplings is introduced. As applications, two kinds of discrete integrable couplings of the resulting system are worked out.
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supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800)the Science Foundation of the Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806)+1 种基金the Shanghai Leading Academic Discipline Project (Grant No. J50101)the Key Disciplines of Shanghai Municipality (S30104)
文摘Based on the constructed Lie superalgebra, the super-classical-Boussinesq hierarchy is obtained. Then, its super- Hamiltonian structure is obtained by making use of super=trace identity. Furthermore, the super-classical-Boussinesq hierarchy is also integrable in the sense of Liouville.
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.
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.
