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| Anderson R.L., Ibragimov N.H. — Lie-Bäcklund transformations in applications |
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| Предметный указатель |
Anharmonic oscillator 93—94
Burger's equations 36
Conservation law 68 115
Conserved vector 68
Constant of the motion 114
Defining equation 62
Dirac equations 74—77
Equivalence of Lie and Lie — Baecklund operators 56
Equivalence, classes of Lie — Baecklund operators 56
Euler equations 68
Example of Clairin 36
Group equivalence of ordinary differential equations 57—59 84—97
Group equivalence of partial differential equations 97—106
Heat equation 55 104
Higher-order variational problems 81—82
Ideal polytropic gas flow 77—79
Infinite set of conservation laws 116
Invariance of functionals 69
Invariance of systems of differential equations 62
Invariance of tangent structure 3 6 9 38 39 42 47
Invariance, relatively G-invariant 83
Korteweg — de Vries equation 25—29 33—35 111—114
Lie tangent operator 41 58
Lie-Baecklund equations 52
Lie-Baecklund operator 50
Liouville's equation 31—33
Miura transformation 35
Modified Korteweg — de Vries equation 29—30 33—35
Motion of a free particle in De Sitter space 70—73
| Newtonian free particle, maximal space-time invariance algebra 91
Newtonian free particle, maximal space-time invariance group 90
O(4) invariance algebra of Fock, angular momentum operator 65
O(4) invariance algebra of Fock, Runge — Lenz operator 65
One-body Keplerian problem 95—97
Perfect incompressible fluid flow 79—80
Quantal free particle 102—103 105
Quantal particle in a uniform external field 103 105—106
Realizations of integrable Lie — Baecklund equations 53—55
Schroedinger equation, time-dependent 100—106
Schroedinger equation, time-independent 64—66
Shallow-water flow 80—81
Sine-Gordon 16 20—25 108—111 115
Surfaces of constant negative curvature 17
Transformation groups, higher-order tangent 41
Transformation groups, Lie point 39
Transformation groups, Lie tangent 38
Transformation groups, Lie — Baecklund tangent 47
Transformations, Baecklund 15—19 19—36
Transformations, Bianchi 12
Transformations, Bianchi — Lie 13
Transformations, kth order 6
Transformations, Lie tangent 3
Transformations, Lie — Baecklund 2
Transformations, Lie — Baecklund tangent 9
Transformations, osculating 7
Transformations, prolongation 3
Unsteady transonic gas motion 73—74
Weak Lagrangian 82
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