Some reductions from a Lax integrable system and their Hamiltonian structures

Abstract A Lie algebra is constructed and an isospectral problem with eight potentials is designed. From which, corresponding hierarchy of nonlinear evolution equation is derived and the integrable couplings of AKNS, D-AKNS, TD, Levi, Li, Ma and Fan hierarchies are deduced, and they are integrable in sense of Liouville. For each reduction case the relevant Hamiltonian structure is established by means of quadratic-form identity.

[1]  Yufeng Zhang,et al.  The quadratic-form identity for constructing the Hamiltonian structure of integrable systems , 2005 .

[2]  屠规彰,et al.  THE TRACE IDENTITY, A POWERFUL TOOL FOR CONSTRUCTING THE HAMILTONIAN STRUCTURE OF INTEGRABLE SYSTEMS (II) , 1989 .

[3]  Zhang Mathematics.  Integrable Couplings and Hamiltonian Structure of the AKNS-KN Soliton-Equation Hierarchy , 2008 .

[4]  夏铁成,et al.  Multi-component Dirac equation hierarchy and its multi-component integrable couplings system , 2007 .

[5]  En-gui Fan.  Some New Reductions From a Lax Integrable System , 2002 .

[6]  Huanhe Dong,et al.  Two types of multicomponent matrix loop algebras and its application , 2007 .

[7]  张玉峰.  An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system , 2005 .

[8]  Gui‐zhang Tu,et al.  The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems , 1989 .

[9]  Zhang Yufeng.  An integrable Hamiltonian hierarchy, a high-dimensional loop algebra and associated integrable coupling system , 2003 .

[10]  Dazhi Meng,et al.  The trace identity, a powerful tool for constructing the hamiltonian structure of integrable systems (II) , 1989 .

[11]  Zhang Yufeng,et al.  A type of expanding integrable system for NLS-mKdV hierarchy , 2003 .

[12]  董焕河.  Discrete integrable couplings associated with modified Korteweg--de Vries lattice and two hierarchies of discrete soliton equations , 2007 .