An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of th...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierar...The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identi...Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction,special cases of this nonlinear super integrable couplings were obtained.展开更多
Nonlinear super integrable couplings of the super Yang hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity. ...Nonlinear super integrable couplings of the super Yang hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of Yang hierarchy were obtained.展开更多
Based upon the basis of Lie super algebra B(0,1), the super Tu equation hierarchy with self-con- sistent sources was presented. Furthermore, the infinite conservation laws of above hierarchy were given.
Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identit...Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identity. As its reduction, special cases of this nonlinear super integrable coupling were obtained.展开更多
This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which ...This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.展开更多
By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries（NLS-mKdV） hierarchy with self-consistent sou...By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries（NLS-mKdV） hierarchy with self-consistent sources as well as its nonlinear integrable couplings are derived.With the help of the variational identity,their Hamiltonian structures are generated.展开更多
An extension of the Lie algebra A_~n-1 has been proposed [Phys. Lett. A, 2003, [STHZ]310:19-24]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra [AKG～]. Based on the loo...An extension of the Lie algebra A_~n-1 has been proposed [Phys. Lett. A, 2003, [STHZ]310:19-24]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra [AKG～]. Based on the loop algebra [AKG～], the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.展开更多
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147 and 11071159)the Natural Science Foundation of Shanghai,China (Grant No.09ZR1410800)+2 种基金the Science Foundation of the Key Laboratory of Mathematics Mechanization,China (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project,China (Grant No.J50101)the Key Disciplines of Shanghai Municipality of China (Grant No.S30104)
文摘The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
基金Supported by the Natural Science Foundation of Henan Province（162300410075） the Science and Technology Key Research Foundation of the Education Department of Henan Province（14A110010） the Youth Backbone Teacher Foundationof Shangqiu Normal University（2013GGJS02）
文摘Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity, and the conserved functionals were proved to be in involution in pairs under the defined Poisson bracket. As its reduction,special cases of this nonlinear super integrable couplings were obtained.
文摘Nonlinear super integrable couplings of the super Yang hierarchy based upon an enlarged matrix Lie super algebra were constructed. Then its super Hamiltonian structures were established by using super trace identity. As its reduction, nonlinear integrable couplings of Yang hierarchy were obtained.
文摘Based upon the basis of Lie super algebra B(0,1), the super Tu equation hierarchy with self-con- sistent sources was presented. Furthermore, the infinite conservation laws of above hierarchy were given.
基金ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China （No.61072147）, the Natural Science Foundation of Henan Province （No.132300410202）, the Science and Technology Key Research Foundation of the Education DeparuHent of Henan Province （No. 12A 110017） and the Youth Research Foundation of Shangqiu Normal University （No. 2011QN12）.
文摘Nonlinear super integrable couplings of a super integrable hierarchy based upon an enlarged matrix Lie super algebra were constructed. And its super Hamiltonian structures were established by using super trace identity. As its reduction, special cases of this nonlinear super integrable coupling were obtained.
基金supported by the National Key Basic Research Development of China (Grant No 2004CB318000)
文摘This paper presents a set of multicomponent matrix Lie algebra, which is used to construct a new loop algebra A^-M. By using the Tu scheme, a Liouville integrable multicomponent equation hierarchy is generated, which possesses the Hamiltonian structure. As its reduction cases, the multicomponent （2＋1）-dimensional Glachette-Johnson （G J） hierarchy is given. Finally, the super-integrable coupling system of multicomponent （2＋1）-dimensional GJ hierarchy is established through enlarging the spectral problem.
基金The National Natural Science Foundation of China(1154717511271008+1 种基金11501526)the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China(2017GGJS145)
基金Project supported by the Innovation Group Project of the Chinese Academy of Sciences (Grant No. KZCX2-YW-Q07-01)the Key Foundation of the National Natural Science Foundation of China (Grant No. 41030855)the Special Funding of Marine Science Study,State Ocean Administration of China (Grant No. 20090513-2)
文摘By means of the Lie algebra B 2,a new extended Lie algebra F is constructed.Based on the Lie algebras B 2 and F,the nonlinear Schro¨dinger-modified Korteweg de Vries（NLS-mKdV） hierarchy with self-consistent sources as well as its nonlinear integrable couplings are derived.With the help of the variational identity,their Hamiltonian structures are generated.
文摘An extension of the Lie algebra A_~n-1 has been proposed [Phys. Lett. A, 2003, [STHZ]310:19-24]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra [AKG～]. Based on the loop algebra [AKG～], the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.
