孤子耦合方程族的代数结构、自相溶源和守恒律（英文版）
出版时间:
2017-01
版次:
1
ISBN:
9787030515148
定价:
78.00
装帧:
平装
开本:
16开
纸张:
胶版纸
页数:
181页
正文语种:
英语
1人买过
-
The main contents of the book include the following： In chapter 2， we would liketo present a definition of the bi-integrable couplings of continuous and discrete solitonhierarchies， which contain two given integrable equations as their sub-systems. Thereare much richer mathematical structures behind bi-integrable couplings than scalarintegrable equations. And it is shown that such bi-integrable coupling system canpossess zero curvature representation and algebraic structure associated with semi-direct sums of Lie algebras. As application examples of the algebraic structure， thebi-integrable coupling system of the MKdV and generalized Toda lattice equationhierarchies are presented from this theory.
In chapter 3，it is shown that the Kronecker product of matrix Lie algebra canbe applied to construct a new integrable coupling system and Hamiltonian struc-tures of continuous and discrete soliton hierarchies. Furthermore， we construct theHamiltonian structure of integrable couplings of soliton hierarchy by using the Kro-necker product. The key steps aim at constructing a new Lax pairs by the Kroneckerproduct. As illustrate examples， direct application to the continuous and discretespectral problems lead to some novel soliton equation hierarchies of integrable cou-pling system. Then， we present the Hamiltonian structure of integrable couplings ofcontinuous and discrete hierarchies with the component-trace identity. Chapter 1 Introduction
1．1 Discovery and development of the soliton
1．2 Development situation of integrable system
1．3 Development of exact solution in nonlinear evolution equation
Chapter 2 Algebraic Structure of a Coupled Soliton Equation Hierarchy
2．1 Kac-Moody algebra
2．1．1 Single Lie algebra Al
2．1．2 Affine Lie algebra Al（1）
2．1．3 Symmetry， Loop algebra and Virasoro algebra
2．2 Algebraic structure of Lax represention of zero curvature equation
2．3 Algebraic structure of bi-integrable couplings of soliton hierarchy
2．3．1 The algebraic structure of bi-integrable coupling system
2．3．2 Bi-integrable coupling system of the MKdV equation hierarchy
2．4 A bi-integrable couplings of discrete soliton hierarchy
2．4．1 Bi-integrable coupling system for discrete soliton hierarchy
2．4．2 Bi-integrable coupling system of the generalized Toda lattice equation hierarchy
Chapter 3 An Integrable Couplings of Soliton Hierarchy with Kronecker Product
3．1 An integrable couplings of AKNS hierarchy with Kronecker product．
3．1．1 An integrable couplings with Kronecker product
3．1．2 Integrable couplings of the AKNS hierarchy with Kronecker product
3．1．3 Hamiltonian structure of the integrable couplings with Kronecker product
3．2 A nonlinear integrable couplings of KdV soliton hierarchy
3．3 Integrable couplings for non-isospectral AKNS equation hierarchy
3．4 An integrable couplings for discrete soliton equation with Kronecker product
3．4．1 An integrable couplings of discrete soliton equation
3．4．2 Integrable couplings of the Toda lattice hierarchy
3．4．3 Hamiltonian structures of the discrete integrable couplings with Kronecker product
3．5 A Volterra lattice equation hierarchy and its integrable couplings
3．5．1 A new discrete integrable couplings with Kronecker product
3．5．2 Integrable coupling system of the nonlinear equation hierarchy
3．6 On the relation a lattice hierarchy and the continuous soliton hierarchy
3．6．1 Integrable equation hierarchy of continuous and multicomponent AKNS hierarchy
3．6．2 On the relation of a new multicomponent lattice hierarchy and the multicomponent AKNS hierarchy
Chapter 4 An Integrable Coupled Hierarchy with Self-consistent Sources
4．1 An integrable couplings of TD hierarchy with self-consistent sources
4．1．1 A super-integrable system of soliton equation hierarchy with self-consistent sources
4．1．2 A super-integrable TD hierarchy with self-consistent sources and its Hamiltonian functions
4．1．3 Bi-nonlineartion of the integrable couplings of the TD hierarchy
4．2 Integrable couplings of generalized WKI hierarchy with self-consistent sources
4．2．1 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 sources
4．3．1 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 3x3 discrete soliton hierarchy with self-consistent sources
4．4．1 A discrete soliton hierarchy with self-consistent sources for 3 x 3 Lax pairs
4．4．2 A new 3x3 lattice soliton hierarchy with self-consistent sources
Chapter 5 Conservation Laws of a Nonlinear Integrable Couplings
5．1 Conservation laws of a nonlinear integrable couplings of AKNS soliton hierarchy
5．1．1 A nonlinear integrable couplings and its conservation laws
5．1．2 Conservation laws for the nonlinear integrable couplings of AKNS hierarchy
5．2 Conservation laws and self-consistent sources for a super classical Boussinesq hierarchy
5．2．1 A super matrix Lie algebra and a super soliton hierarchy with self-consistent sources
5．2．2 The super classical Boussinesq hierarchy with self-consistent sources and conservation laws
5．3 A nonlinear integrable couplings of C-KdV soliton hierarchy and its infinite conservation laws
5．3．1 A nonlinear integrable couplings of the C-KdV hierarchy
5．3．2 Conservation laws for the nonlinear integrable couplings of C-KdV hierarchy
5．4 Infinite conservation laws for a nonlinear integrable couplings of Toda hierarchy
5．4．1 Nonlinear integrable couplings of the generalized Toda lattice hierarchy and its conservation laws
5．4．2 Infinite conservation laws for the nonlinear integrable couplingsof Toda lattice hierarchy
Bibliography
-
内容简介:
The main contents of the book include the following： In chapter 2， we would liketo present a definition of the bi-integrable couplings of continuous and discrete solitonhierarchies， which contain two given integrable equations as their sub-systems. Thereare much richer mathematical structures behind bi-integrable couplings than scalarintegrable equations. And it is shown that such bi-integrable coupling system canpossess zero curvature representation and algebraic structure associated with semi-direct sums of Lie algebras. As application examples of the algebraic structure， thebi-integrable coupling system of the MKdV and generalized Toda lattice equationhierarchies are presented from this theory.
In chapter 3，it is shown that the Kronecker product of matrix Lie algebra canbe applied to construct a new integrable coupling system and Hamiltonian struc-tures of continuous and discrete soliton hierarchies. Furthermore， we construct theHamiltonian structure of integrable couplings of soliton hierarchy by using the Kro-necker product. The key steps aim at constructing a new Lax pairs by the Kroneckerproduct. As illustrate examples， direct application to the continuous and discretespectral problems lead to some novel soliton equation hierarchies of integrable cou-pling system. Then， we present the Hamiltonian structure of integrable couplings ofcontinuous and discrete hierarchies with the component-trace identity.
-
目录:
Chapter 1 Introduction
1．1 Discovery and development of the soliton
1．2 Development situation of integrable system
1．3 Development of exact solution in nonlinear evolution equation
Chapter 2 Algebraic Structure of a Coupled Soliton Equation Hierarchy
2．1 Kac-Moody algebra
2．1．1 Single Lie algebra Al
2．1．2 Affine Lie algebra Al（1）
2．1．3 Symmetry， Loop algebra and Virasoro algebra
2．2 Algebraic structure of Lax represention of zero curvature equation
2．3 Algebraic structure of bi-integrable couplings of soliton hierarchy
2．3．1 The algebraic structure of bi-integrable coupling system
2．3．2 Bi-integrable coupling system of the MKdV equation hierarchy
2．4 A bi-integrable couplings of discrete soliton hierarchy
2．4．1 Bi-integrable coupling system for discrete soliton hierarchy
2．4．2 Bi-integrable coupling system of the generalized Toda lattice equation hierarchy
Chapter 3 An Integrable Couplings of Soliton Hierarchy with Kronecker Product
3．1 An integrable couplings of AKNS hierarchy with Kronecker product．
3．1．1 An integrable couplings with Kronecker product
3．1．2 Integrable couplings of the AKNS hierarchy with Kronecker product
3．1．3 Hamiltonian structure of the integrable couplings with Kronecker product
3．2 A nonlinear integrable couplings of KdV soliton hierarchy
3．3 Integrable couplings for non-isospectral AKNS equation hierarchy
3．4 An integrable couplings for discrete soliton equation with Kronecker product
3．4．1 An integrable couplings of discrete soliton equation
3．4．2 Integrable couplings of the Toda lattice hierarchy
3．4．3 Hamiltonian structures of the discrete integrable couplings with Kronecker product
3．5 A Volterra lattice equation hierarchy and its integrable couplings
3．5．1 A new discrete integrable couplings with Kronecker product
3．5．2 Integrable coupling system of the nonlinear equation hierarchy
3．6 On the relation a lattice hierarchy and the continuous soliton hierarchy
3．6．1 Integrable equation hierarchy of continuous and multicomponent AKNS hierarchy
3．6．2 On the relation of a new multicomponent lattice hierarchy and the multicomponent AKNS hierarchy
Chapter 4 An Integrable Coupled Hierarchy with Self-consistent Sources
4．1 An integrable couplings of TD hierarchy with self-consistent sources
4．1．1 A super-integrable system of soliton equation hierarchy with self-consistent sources
4．1．2 A super-integrable TD hierarchy with self-consistent sources and its Hamiltonian functions
4．1．3 Bi-nonlineartion of the integrable couplings of the TD hierarchy
4．2 Integrable couplings of generalized WKI hierarchy with self-consistent sources
4．2．1 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 sources
4．3．1 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 3x3 discrete soliton hierarchy with self-consistent sources
4．4．1 A discrete soliton hierarchy with self-consistent sources for 3 x 3 Lax pairs
4．4．2 A new 3x3 lattice soliton hierarchy with self-consistent sources
Chapter 5 Conservation Laws of a Nonlinear Integrable Couplings
5．1 Conservation laws of a nonlinear integrable couplings of AKNS soliton hierarchy
5．1．1 A nonlinear integrable couplings and its conservation laws
5．1．2 Conservation laws for the nonlinear integrable couplings of AKNS hierarchy
5．2 Conservation laws and self-consistent sources for a super classical Boussinesq hierarchy
5．2．1 A super matrix Lie algebra and a super soliton hierarchy with self-consistent sources
5．2．2 The super classical Boussinesq hierarchy with self-consistent sources and conservation laws
5．3 A nonlinear integrable couplings of C-KdV soliton hierarchy and its infinite conservation laws
5．3．1 A nonlinear integrable couplings of the C-KdV hierarchy
5．3．2 Conservation laws for the nonlinear integrable couplings of C-KdV hierarchy
5．4 Infinite conservation laws for a nonlinear integrable couplings of Toda hierarchy
5．4．1 Nonlinear integrable couplings of the generalized Toda lattice hierarchy and its conservation laws
5．4．2 Infinite conservation laws for the nonlinear integrable couplingsof Toda lattice hierarchy
Bibliography
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