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    孤子耦合方程族的代数结构.自相溶源和守恒律
    丛书名: 沈阳师范大学学术文库系列丛书 ISBN: 978-7-03-051514-8
    供应商: 科学出版社 出版日期: 2017年4月1日
    编著者: 于发军 译者:
    版次: 1 印次: 1
    页数: 0 语种:
    纸张: 包装: 平装
    开本: 32开 读者对象:
    原价: ¥78.00 折扣价: ¥56.20    立刻节省:¥21.80
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    内容提要
    The maicontents of the book include the following: Ichapter 2, we would liketo present a definitioof the bi-integrable couplings of continuous and discrete solitonhierarchies, which contaitwo giveintegrable equations as their sub-systems. Thereare much richer mathematical structures behind bi-integrable couplings thascalarintegrable equations. And it is showthat such bi-integrable coupling system canpossess zero curvature representatioand algebraic structure associated with semi-direct sums of Lie algebras. As applicatioexamples of the algebraic structure, thebi-integrable coupling system of the MKdV and generalized Toda lattice equationhierarchies are presented from this theory.
      Ichapter 3,it is showthat the Kronecker product of matrix Lie algebra canbe applied to construct a new integrable coupling system and Hamiltoniastruc-tures of continuous and discrete solitohierarchies. Furthermore, we construct theHamiltoniastructure of integrable couplings of solitohierarchy by using the Kro-necker product. The key steps aim at constructing a new Lax pairs by the Kroneckerproduct. As illustrate examples, direct applicatioto the continuous and discretespectral problems lead to some novel solitoequatiohierarchies of integrable cou-pling system. Then, we present the Hamiltoniastructure 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 situatioof integrable system
    1.3 Development of exact solutioinonlinear evolutioequation

    Chapter 2 Algebraic Structure of a Coupled SolitoEquatioHierarchy
    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 representioof zero curvature equation
    2.3 Algebraic structure of bi-integrable couplings of solitohierarchy
    2.3.1 The algebraic structure of bi-integrable coupling system
    2.3.2 Bi-integrable coupling system of the MKdV equatiohierarchy
    2.4 A bi-integrable couplings of discrete solitohierarchy
    2.4.1 Bi-integrable coupling system for discrete solitohierarchy
    2.4.2 Bi-integrable coupling system of the generalized Toda lattice equatiohierarchy

    Chapter 3 AIntegrable Couplings of SolitoHierarchy with Kronecker Product
    3.1 Aintegrable couplings of AKNS hierarchy with Kronecker product.
    3.1.1 Aintegrable couplings with Kronecker product
    3.1.2 Integrable couplings of the AKNS hierarchy with Kronecker product
    3.1.3 Hamiltoniastructure of the integrable couplings with Kronecker product
    3.2 A nonlinear integrable couplings of KdV solitohierarchy
    3.3 Integrable couplings for non-isospectral AKNS equatiohierarchy
    3.4 Aintegrable couplings for discrete solitoequatiowith Kronecker product
    3.4.1 Aintegrable couplings of discrete solitoequation
    3.4.2 Integrable couplings of the Toda lattice hierarchy
    3.4.3 Hamiltoniastructures of the discrete integrable couplings with Kronecker product
    3.5 A Volterra lattice equatiohierarchy and its integrable couplings
    3.5.1 A new discrete integrable couplings with Kronecker product
    3.5.2 Integrable coupling system of the nonlinear equatiohierarchy
    3.6 Othe relatioa lattice hierarchy and the continuous solitohierarchy
    3.6.1 Integrable equatiohierarchy of continuous and multicomponent AKNS hierarchy
    3.6.2 Othe relatioof a new multicomponent lattice hierarchy and the multicomponent AKNS hierarchy

    Chapter 4 AIntegrable Coupled Hierarchy with Self-consistent Sources
    4.1 Aintegrable couplings of TD hierarchy with self-consistent sources
    4.1.1 A super-integrable system of solitoequatiohierarchy with self-consistent sources
    4.1.2 A super-integrable TD hierarchy with self-consistent sources and its Hamiltoniafunctions
    4.1.3 Bi-nonlineartioof 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 equatiohierarchy with self-consistent sources associated with sl(4)
    4.3 Aintegrable couplings of Yang solitohierarchy with self-consistent sources
    4.3.1 Aintegrable couplings of solitoequatiohierarchy with self-consistent sources associated with sl(4)
    4.3.2 Yang equatiohierarchy with self-consistent sources associated with sl(2)
    4.4 A new 3x3 discrete solitohierarchy with self-consistent sources
    4.4.1 A discrete solitohierarchy with self-consistent sources for 3 x 3 Lax pairs
    4.4.2 A new 3x3 lattice solitohierarchy with self-consistent sources

    Chapter 5 ConservatioLaws of a Nonlinear Integrable Couplings
    5.1 Conservatiolaws of a nonlinear integrable couplings of AKNS solitohierarchy
    5.1.1 A nonlinear integrable couplings and its conservatiolaws
    5.1.2 Conservatiolaws for the nonlinear integrable couplings of AKNS hierarchy
    5.2 Conservatiolaws and self-consistent sources for a super classical Boussinesq hierarchy
    5.2.1 A super matrix Lie algebra and a super solitohierarchy with self-consistent sources
    5.2.2 The super classical Boussinesq hierarchy with self-consistent sources and conservatiolaws
    5.3 A nonlinear integrable couplings of C-KdV solitohierarchy and its infinite conservatiolaws
    5.3.1 A nonlinear integrable couplings of the C-KdV hierarchy
    5.3.2 Conservatiolaws for the nonlinear integrable couplings of C-KdV hierarchy
    5.4 Infinite conservatiolaws for a nonlinear integrable couplings of Toda hierarchy
    5.4.1 Nonlinear integrable couplings of the generalized Toda lattice hierarchy and its conservatiolaws
    5.4.2 Infinite conservatiolaws for the nonlinear integrable couplingsof Toda lattice hierarchy
    Bibliography
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