Miva T. — Solitons : Differential equations, symmetries and infinite dimensional algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Miva T. — Solitons : Differential equations, symmetries and infinite dimensional algebras

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Название: Solitons : Differential equations, symmetries and infinite dimensional algebras

Автор: Miva T.

Аннотация:

This book investigates the high degree of symmetry that lies hidden in integrable systems. To that end, differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems. Chapters discuss the work of M. Sato on the algebraic structure of completely integrable systems, together with developments of these ideas in the work of M. Kashiwara. The text should be accessible to anyone with a knowledge of differential and integral calculus and elementary complex analysis, and it will be a valuable resource to both novice and expert alike.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 108

Добавлена в каталог: 22.09.2005

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Предметный указатель

Affine Lie algebra $\hat{sl_{2}}$       61 64 65 104
Annihilation operator      33—41 45 50 59 80
Anticommutator      34 54 77
Anticommutator bracket      46
Bilinear identity      28—29 58—60 76 80 81 88
Boson      33—35 43 46 63
Boson — Fermion correspondence      43 50 57—58 81 82 84
Bosonic algebra      32
Bosonic commutation relations      46
Bosonic Fock space      33 47 49 52 57 88
Bosonic normal product      45
Canonical anticommutation relation      34 36 76
Canonical commutation relation      32—34 46
Cauchy's identity      44 51
CHARACTER      52 84 99
Character polynomial      76 82—85 87—93
Charge      37 39 40 47 50 55 57 77 79—82 84 86—89 99 101 102
Charged Young diagram      86
Clifford algebra      34—35 41 45 76 87
Clifford conjugation      78
Clifford group      76—78
Cocycle condition      56 60
Colon notation      45
Commutator      41 54 56 96
Commutator bracket      4 8 31 46 54—56 64
Complex projective line      67
Complex projective space      67
Creation operator      33 34 36—38 40—41 50
Differential equation      3 5 32 93
Differential polynomial      6—7
Dirac's sea      37
Dual wave function      58
Eigenvalue      8 9
Electric charge      see "Charge"
Energy      37 39 40 47 52 77 99
EXPONENT      4 21 23
Fermion      32 34—36 43
Fermionic Fock space      36 49
Fock representation      35 37 41
Fock space      37 46—47 76 80
Frame      68 100
Generating function      43 46 50—52 57
Grassmannian      66 68 69 75 76 80
Group      1 2 5
Group action      ix 3 53
Heisenberg algebra      33—35 64
Higher order KdV equation      9 13 23
Hirota bilinear method      viii 19 27 92—93
Hirota derivative      ix 19—24
Hirota equation      19—23 53 60 61 65 88 90 92—93
Homogeneous      91 96
Homogeneous coordinates      69—70

Homogeneous differential polynomial      7
Homogeneous polynomial      44
Infinite dimensional Grassmannian      ix 76 88
Infinite dimensional group      ix 53
Infinite dimensional Lie algebra      53 65 104
Infinite dimensional symmetries      ix 5 14 32
Infinitesimal generator      3—5 7
Infinitesimal transformation      1 3—5 9 15 25 32 59—61 63—65
Integrable system      viii—ix 22 105
KdV equation      vii—ix 1 5—7 9 11 15 19—24 31 32 61 63—65 105
KdV hierarchy      15 23—25 27 61
KP equation      ix 27 32 53 57 59—60 105
KP hierarchy      16 17 27—29 31 58 60 61 63 76 90 92
Lax form      8—10 13 59
Level      65 104
Lie algebra      3—5 53 54 56—58 60 63—65 80 97
Linear differential equation      vii viii 8 61
Maya diagram      35—37 82 85—87 89—90
Nonlinear differential equation      viii ix 17
Normal product      44—46 55 96 98
Operator algebras      32—33 44 57 103
Orbit      53—54 58 60 64 65 76 79 80 90 99
Parabolic subgroup      68
Pluecker      69
Pluecker coordinates      69—72 75 76 92 100—101
Pluecker embedding      70
Pluecker relations      66 71—76 80—82 88 90—93 102
Point at infinity      67
Projective geometry      66
Projective line      67
Projective pseudodifferential operator      11—13 16—18 61
Projective space      67 68 70 72
Quantum field theory      43 104—105
Quantum group      106
Representation      33 35 57 58 65 82 84 103 104
Signed Maya diagram      89—90
Soliton      viii 32 103
Soliton equation      viii 19 65 103 105
Soliton solution      21—22 25—27 31 60 61 63 104
Spectral variable      8
Symmetry      ix 1—2 4—7 9 14—15 23—24 32 53
Tau function      17 22 25 27—31 53 58—60 63 65 76 88 90—93 105
Toda lattice      viii
Transformation group      ix 1—2 5 53 58 61 63
Vacuum expectation value      40—41 43
Vacuum orbit      80
Vacuum state      33 34 36—39 41 46 58 64 65 76—77 79—81 90
Vacuum vector      41 53 80
Vertex operator      19 24 25 27 57 60 63—64 97 104 106
Wave function      58 60
Wick's theorem      41 44 59 85 88 98
Young diagram      82—88 91 102

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