Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational ide...Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.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
In this paper, a new nonlinear integrable coupling system of the soliton hierarchy is presented. Prom the Lax pairs, the coupled KdV equations are constructed successfully. Based on the prolongation method of Wahlquis...In this paper, a new nonlinear integrable coupling system of the soliton hierarchy is presented. Prom the Lax pairs, the coupled KdV equations are constructed successfully. Based on the prolongation method of Wahlquist and Estabrook, we study the prolongation structure of the nonlinear integrable couplings of the KdV equation.展开更多
How to construct new super integrable equation hierarchy is an important problem.In this paper,a new Lax pair is proposed and the super D-Kaup-Newell hierarchy is generated,then a nonlinear integrable coupling of the ...How to construct new super integrable equation hierarchy is an important problem.In this paper,a new Lax pair is proposed and the super D-Kaup-Newell hierarchy is generated,then a nonlinear integrable coupling of the super D-Kaup-Newcll hierarchy is constructed.The super Hamiltonian structures of coupling equation hierarchy is derived with the aid of the super variational identity.Finally,the self-consistent sources of super integrable coupling hierarchy is established.It is indicated that this method is a straightforward and efficient way to construct the super integrable equation hierarchy.展开更多
We construct a nonlinear integrable coupling of discrete soliton hierarchy, and establish the infinite conservation laws （CLs） for the nonlinear integrable coupling of the lattice hierarchy. As an explicit applicati...We construct a nonlinear integrable coupling of discrete soliton hierarchy, and establish the infinite conservation laws （CLs） for the nonlinear integrable coupling of the lattice hierarchy. As an explicit application of the method proposed in the paper, the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.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 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
We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its r...We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its reduction,we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.展开更多
Based on a kind of Lie a/gebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using th...Based on a kind of Lie a/gebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy.展开更多
Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time...Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.展开更多
基金Supported by the Fundamental Research Funds of the Central University under Grant No. 2010LKS808the Natural Science Foundation of Shandong Province under Grant No. ZR2009AL021
文摘Two new explicit Lie algebras are introduced for which the nonlinear integrable couplings of the Giachetti- Johnson （G J） hierarchy and the Yang hierarchy are obtained, respectively. By employing the variational identity their ttamiltonian structures are also generated. The approach presented in the paper can also provide nonlinear integrable couplings of other soliton hierarchies of evolution equations.
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.
基金Project supported by the Scientific Research Fundation of the Education Department of Liaoning Province,China(GrantNo.L2010513)the China Postdoctoral Science Foundation(Grant No.2011M500404)
文摘In this paper, a new nonlinear integrable coupling system of the soliton hierarchy is presented. Prom the Lax pairs, the coupled KdV equations are constructed successfully. Based on the prolongation method of Wahlquist and Estabrook, we study the prolongation structure of the nonlinear integrable couplings of the KdV equation.
基金The authors thank Yan Zhang for helpful advices during the writing of this paper.This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11547175,11975145)the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China(2017GGJS145).
文摘How to construct new super integrable equation hierarchy is an important problem.In this paper,a new Lax pair is proposed and the super D-Kaup-Newell hierarchy is generated,then a nonlinear integrable coupling of the super D-Kaup-Newcll hierarchy is constructed.The super Hamiltonian structures of coupling equation hierarchy is derived with the aid of the super variational identity.Finally,the self-consistent sources of super integrable coupling hierarchy is established.It is indicated that this method is a straightforward and efficient way to construct the super integrable equation hierarchy.
基金Project supported by the Postdoctoral Science Foundation of China (Grant No. 2011M500404 )the Program for Liaoning Excellent Talents in University,China (Grant No. LJQ2011119)
文摘We construct a nonlinear integrable coupling of discrete soliton hierarchy, and establish the infinite conservation laws （CLs） for the nonlinear integrable coupling of the lattice hierarchy. As an explicit application of the method proposed in the paper, the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.
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 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 Natural Science Foundation of China under Grant No. 60972164the Program for Liaoning Excellent Talents in University under Grant No. LJQ2011136+2 种基金the Key Technologies R&D Program of Liaoning Province under Grant No. 2011224006the Program for Liaoning Innovative Research Team in University under Grant No. LT2011019the Science and Technology Program of Shenyang under Grant No. F11-264-1-70
文摘We construct nonlinear super integrable couplings of the super integrable Dirac hierarchy based on an enlarged matrix Lie superalgebra.Then its super Hamiltonian structure is furnished by super trace identity.As its reduction,we gain the nonlinear integrable couplings of the classical integrable Dirac hierarchy.
基金Supported by the Natural Science Foundation of China under Grant Nos.11271008,61072147,11071159the Shanghai Leading Academic Discipline Project under Grant No.J50101the Shanghai Univ.Leading Academic Discipline Project(A.13-0101-12-004)
文摘Based on a kind of Lie a/gebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy.
基金Supported by National Natural Science Foundation of China under Grant Nos.11271168 and 11671177by the Priority Academic Program Development of Jiangsu Higher Education Institutionsby Innovation Project of the Graduate Students in Jiangsu Normal University
文摘Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.
