[按需印刷]孤子耦合方程族的代数结构、自相溶源和守恒律(英文版)/于发军科学出版社

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孤子耦合方程族的代数结构、自相溶源和守恒律(英文版)
	ISBN	9787030515148
	定价	78
	作者	于发军 著; 编; 译;
	开本	B5
	装帧	平装
	页数	192
	出版时间	2017年03月
	出版社	科学出版社

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Contents
Chapter l Introduction 1
1.1 Discovery and development of the soliton 1
1.2 Development situation of integrable system 3
1.3 Development of exact solution in nonlinear evolution equation 6
Chapter 2 Algebraic Structure of a Coupled Soliton Equation Hierarchy 9
2.1 KacMoody algebra 9
2.1.1 Single Lie algebra Az 10
2.1.2 Affine Lie alge ra Ai(1) 12
2.1.3 Symmetry, Loop algebra and Virasoro algebra 15
2.2 Algebraic structure of Lax represention of zero curvature equation 15
2.3 Algebraic structure of biintegrable couplings of soliton hierarchy 19
2.3.1 The algebraic structure of biintegrable coupling system 21
2.3.2 Biintegrable coupling system of the MKdV equation hierarchy 27
2.4 A biintegrable couplings of discrete soliton hierarchy 33
2.4.1 Biintegrable coupling system for discrete soliton hierarchy 34
2.4.2 Biintegrable coupling system of the generalized Toda lattice equation hierarchy 36
Chapter 3 An Integrable Couplings of Soliton Hierarchy with Kronecker Product 42
3.1 An integrable couplings of AKNS hierarchy with Kronecker product 42
3.1.1 An integrable couplings with Kronecker product 42
3.1.2 Integrable couplings of the AKNS hierarchy with Kronecker product 45
3.1.3 Hamiltonian structure of the integrable couplings with Kronecker product 48
3.2 A nonlinear integrable couplings of KdV soliton hierarchy 52
3.3 Integrable couplings for nonisospectral AKNS equation hierarchy 55
3.4 An integrable couplings for discrete soliton equation with Kronecker product 67
3.4.1 An integrable couplings of discrete soliton equation 67
3.4.2 Integrable couplings of the Toda lattice hierarchy 70
3.4.3 Hamiltonian structures of the discrete integrable couplings with Kronecker product 73
3.5 A Volterra lattice equation hierarchy and its integrable couplings 80
3.5.1 A new discrete integrable couplings with Kronecker product 80
3.5.2 Integrable coupling system of the nonlinear equation hierarchy 81
3.6 0n the relation a lattice hierarchy and the continuous soliton hierarchy 85
3.6.1 Integrable equation hierarchy of continuous and multicomponent AKNS hierarchy 85
3.6.2 0n the relation of a new multicomponent lattice hierarchy and the multicomponent AKNS hierarchy 94
Chapter 4 An Integrable Coupled Hierarchy with Selfconsistent Sources 100
4.1 An integrable couplings of TD hierarchy with selfconsistent sources 100
4.1.1A superintegrable system of soliton equation hierarchy with self consistent sources 100
4.1.2A superintegrable TD hierarchy with selfconsistent sources and its Hamiltonian functions 104
4.1.3 Binonlineartion of the integrable couplings of the TD hierarchy 108
4.2 Integrable couplings of generalized WKI hierarchy with self consistent sources 112
4.2.1 GWKI equations hierarchy with selfconsistent sources associated with
4.2.2 Integrable couplings of the GWKI equation hierarchy with selfconsistent sources associated with sl(4) 119
4.3 An integrable couplings of Yang soliton hierarchy with selfconsistent sources 122
4.3.1 An integrable couplings of soliton equation hierarchy with selfconsistent sources associated with sl(4) 123
4.3.2 Yang equation hierarchy with selfconsistent sources associated with
4.4 A new 3x3 discrete soliton hierarchy with selfconsistent sources 134
4.4.1 A discrete soliton hierarchy with selfconsistent sources for 3x3 Lax pairs 135
4.4.2 A new 3x3 lattice soliton hierarchy with selfconsistent sources 138
Chapter 5 Conservation Laws of a Nonlinear Integrable Couplings 142
5.1 Conservation laws of a nonlinear integrable couplings of AKNS soliton hierarchy 142
5.1.1 A nonlinear integrable couplings and its conservation laws 143
5.1.2 Conservation laws for the nonlinear integrable couplings of AKNS hierarchy 144
5.2 Conservation laws and selfconsistent sources for a super classical Boussinesq hierarchy 151
5.2.1 A super matrix Lie algebra and a super soliton hierarchy with self consistent sources 151
5.2.2 The super classical Boussinesq hierarchy with self consistent sources and conservation laws 154
5.3 A nonlinear integrable couplings of CKdV soliton hierarchy and its infinite conservation laws 160
5.3.1 A nonlinear integrable couplings of the CKdV hierarchy 160
5.3.2 Conservation laws for the nonlinear integrable couplings of CKdV hierarchy 163
5.4 Infinite conservation laws for a nonlinear integrable couplings of Toda hierarchy 166
5.4.1 Nonlinear integrable couplings of the generalized Toda lattice hierarchy and its conservation laws 167
5.4.2 Infinite conservation laws for the nonlinear integrable couplings of Toda lattice hierarchy 171
Bibliography 174


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