孤子耦合方程族的代数结构.自相溶源和守恒律

Chapter 1 Introduction1．1 Discovery and development of the soliton1．2 Development situation of integrable system1．3 Development of exact solution in nonlinear evolution equationChapter 2 Algebraic Structure of a Coupled Soliton Equation Hierarchy2．1 Kac-Moody algebra2．1．1 Single Lie algebra Al2．1．2 Affine Lie algebra Al（1）2．1．3 Symmetry， Loop algebra and Virasoro algebra2．2 Algebraic structure of Lax represention of zero curvature equation2．3 Algebraic structure of bi-integrable couplings of soliton hierarchy2．3．1 The algebraic structure of bi-integrable coupling system2．3．2 Bi-integrable coupling system of the MKdV equation hierarchy2．4 A bi-integrable couplings of discrete soliton hierarchy2．4．1 Bi-integrable coupling system for discrete soliton hierarchy2．4．2 Bi-integrable coupling system of the generalized Toda lattice equation hierarchyChapter 3 An Integrable Couplings of Soliton Hierarchy with Kronecker Product3．1 An integrable couplings of AKNS hierarchy with Kronecker product．3．1．1 An integrable couplings with Kronecker product3．1．2 Integrable couplings of the AKNS hierarchy with Kronecker product3．1．3 Hamiltonian structure of the integrable couplings with Kronecker product3．2 A nonlinear integrable couplings of KdV soliton hierarchy3．3 Integrable couplings for non-isospectral AKNS equation hierarchy3．4 An integrable couplings for discrete soliton equation with Kronecker product3．4．1 An integrable couplings of discrete soliton equation3．4．2 Integrable couplings of the Toda lattice hierarchy3．4．3 Hamiltonian structures of the discrete integrable couplings with Kronecker product3．5 A Volterra lattice equation hierarchy and its integrable couplings3．5．1 A new discrete integrable couplings with Kronecker product3．5．2 Integrable coupling system of the nonlinear equation hierarchy3．6 On the relation a lattice hierarchy and the continuous soliton hierarchy3．6．1 Integrable equation hierarchy of continuous and multicomponent AKNS hierarchy3．6．2 On the relation of a new multicomponent lattice hierarchy and the multicomponent AKNS hierarchyChapter 4 An Integrable Coupled Hierarchy with Self-consistent Sources4．1 An integrable couplings of TD hierarchy with self-consistent sources4．1．1 A super-integrable system of soliton equation hierarchy with self-consistent sources4．1．2 A super-integrable TD hierarchy with self-consistent sources and its Hamiltonian functions4．1．3 Bi-nonlineartion of the integrable couplings of the TD hierarchy4．2 Integrable couplings of generalized WKI hierarchy with self-consistent sources4．2．1 G-WKI equations hierarchy with self-consistent sources associated with sl（2）4．2．2 Integrable couplings of the G-WKI equation hierarchy with self-consistent sources associated with sl（4）4．3 An integrable couplings of Yang soliton hierarchy with self-consistent sources4．3．1 An integrable couplings of soliton equation hierarchy with self-consistent sources associated with sl（4）4．3．2 Yang equation hierarchy with self-consistent sources associated with sl（2）4．4 A new 3×3 discrete soliton hierarchy with self-consistent sources4．4．1 A discrete soliton hierarchy with self-consistent sources for 3 x 3 Lax pairs4．4．2 A new 3×3 lattice soliton hierarchy with self-consistent sourcesChapter 5 Conservation Laws of a Nonlinear Integrable Couplings5．1 Conservation laws of a nonlinear integrable couplings of AKNS soliton hierarchy5．1．1 A nonlinear integrable couplings and its conservation laws5．1．2 Conservation laws for the nonlinear integrable couplings of AKNS hierarchy5．2 Conservation laws and self-consistent sources for a super classical Boussinesq hierarchy5．2．1 A super matrix Lie algebra and a super soliton hierarchy with self-consistent sources5．2．2 The super classical Boussinesq hierarchy with self-consistent sources and conservation laws5．3 A nonlinear integrable couplings of C-KdV soliton hierarchy and its infinite conservation laws5．3．1 A nonlinear integrable couplings of the C-KdV hierarchy5．3．2 Conservation laws for the nonlinear integrable couplings of C-KdV hierarchy5．4 Infinite conservation laws for a nonlinear integrable couplings of Toda hierarchy5．4．1 Nonlinear integrable couplings of the generalized Toda lattice hierarchy and its conservation laws5．4．2 Infinite conservation laws for the nonlinear integrable couplingsof Toda lattice hierarchyBibliography