Dubrovin B.A., Novikov S.P. — Hydrodynamics of soliton lattices :: Электронная библиотека попечительского совета мехмата МГУ

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Dubrovin B.A., Novikov S.P. — Hydrodynamics of soliton lattices

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Название: Hydrodynamics of soliton lattices

Авторы: Dubrovin B.A., Novikov S.P.

Аннотация:

Work carried out during the last few years on the geometry of Hamiltonian systems, including hydrodynamic-type systems and their Poisson brackets, is reviewed. The theory of the integrability of hydrodynamic- type systems is presented. Applications of the formalism developed to problems of the hydrodynamics of weakly deformed soliton lattices — slow modulations of families of periodic and quasiperiodic solutions of nonlinear evolution systems, are described.

Язык:

Рубрика: Физика/Классическая физика/Механика жидкости и газа/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1993

Количество страниц: 136

Добавлена в каталог: 19.06.2005

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Предметный указатель

Abel transformation      19 24 29
Abelian integral      125
Action-angle variables      11—13
Algebra of flows      15 19
Algebraic-geometrical solution      13 24 60 86 107
Analytical Poisson bracket      14—19 23
Anti-involution      17 ff
Average density of topological charge      21
Averaged finite-gap solutions      126—128
Averaging method      64 123 125
Barotropic hydrodynamics      43
Benney equations      44 116 117
Canonical basis of cycles      25 119
Canonical coordinates      8 9
Christoffel symbols      5 39 111
Classical r-matrix      10 11
Clebsch variables      5 34 69 81
Co-cycles in Lie algebra      55 83 84
Completely integrable Hamiltonian system      11 78
Constant brackets      8 33
Differential-geometrical bracket      49 53 112
Differential-geometrical bracket on lattice      57
Equation of state      43
Euler equations      36
Euler — Lagrange equations      8
Euler — Lagrange operator      31
Finite-gap solution      3 22—24 58—60 117
Frobenius algebra      51
Frozen-in fields      37
Gardner — Zakharov — Faddeev Poisson bracket      20 34 82
Gel'fand — Fuks co-cycle      36
Generating function      12
Gurevich — Pitaevskii solution      62 64 89 107 108 122 123 127
Hamilton — Lie group      54—56
Hamiltonian system      3 ff 45
Hodograph transformation      109
Hodograph transformation, generalized      115
Hydrodynamic-type functional      4 5
Hydrodynamic-type systems      3 59
Hydrodynamic-type systems, Hamiltonian      3—5
Hydrodynamic-type systems, non-homogeneous      83
Hydrodynamics of soliton lattice equations      57 58 105
Hyperelliptic Riemann surface      13 17

Invariant scalar product in Lie algebra      51
Jacobi identity      7 8 32—34 40—42 52 75 77
Kac — Moody algebra      35
Kruskal integrals      21 120 124 126
Lax commutational representation      118 124
Leibnitz identity      7 30 39
Lenard — Magri bracket      20 36
Lie bialgebra      54 55
Lie — Poisson bracket      9
Linear brackets      9 36
Lionville tori      11 13 28
Liouville bracket      6 44 61 87 122
Liouville coordinates      6 42 52 61
Liouville's theorem      11 16 19
Local field-theory brackets      30 ff
Local fields      30
Local functional      52
Method of averaging conservation laws      71
Multivalued functional      63 101
Non-linear analogue of WKB method      66 68
Phase space      13
Poisson bracket in magnetic field      8
Poisson bracket of hydrodynamic type      3 ff 37 73
Poisson bracket of hydrodynamic type, degenerate      8 34 87
Poisson bracket of hydrodynamic type, non-degenerate      8 11 40 45 52 53
Quadratic Poisson brackets      10
Quasi-energy      118 119
Quasi-Frobenius algebra      51 52 57
Quasi-momemum      20—22 25 118 119
Relativistic hydrodynamics      80 81 89
Riemann invariants      4 38 60 107 123
Schouten bracket      7
Self-similar solutions      62 89 92 95 107 127 128
Semi-Hamiltonian hydrodynamic-type system      105 115 116
Slow modulations or Whitham's equation      59 ff 89 123
Strongly Liouville bracket      42
Symplectic manifold      7
Symplectic structure      7
System symmetry      109
Theta-function      119
Translationally invariant brackets      31
Ultra-local Poisson bracket      33
Virasoro algebra      36
Yang — Baxter linearized equation      10 11 53

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