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| Matveev V.B., Salle M.A. — Darboux Transformation and Solutions |
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| Предметный указатель |
 -problem 30
Airy, equations 46
Airy, functions 46 47
Background solution 41 55
Baker — Akbiezer functions 37
Benjamin — Ono equation 4 68 71 73 75
Bessel functions 16 83
Binary Darboux transformation 3 19 27 35 47 100
BKcklund transformation 51 88 91
Bloch, equation 59
Bloch, solution 14
Bose gas 51
Boussinesq equation 3 43
Breather 65 90
Burgers equation (BE) 73 74
Burgers equation (BE), lattice version of BE 85
Cauchy problem 3
Crum, formula 14 15
Crum, theorem 9 10 12 16
Cylindrical KdV equation 22 47
Darboux transformation for ![${V}_{\xi} = {U}_{\eta} = [V,U]/2$](/math_tex/0751fdb738a4cb053308968669cbda0782.gif) 49
Darboux transformation for  27
Darboux transformation for ![${\Phi}_{\xi\eta} = i[{\Phi}_{\xi},{\Phi}_{\eta}]$](/math_tex/4f44597ade8f242b6a9dff01a6cdb8b582.gif) 49
Darboux transformation for Benjamin — Ono equation 4 75
Darboux transformation for Bloch equations 55
Darboux transformation for Boussinesque equation 3 44
Darboux transformation for cylindrical KdV equation 3 47 48
Darboux transformation for Davey — Stuartson equation 98
Darboux transformation for discrete nonabelian version of KdV 88
Darboux transformation for discrete version of KdV 84
Darboux transformation for Johnson equation 3 46
Darboux transformation for Kadomtsev — Petviashvili equation 2 3 33 37
Darboux transformation for KdV equation 1 3 31 37
Darboux transformation for KdV type equation 72
Darboux transformation for lattice equations 23
Darboux transformation for lattice Silin — Tikhonchuk equation 94
Darboux transformation for linear matrix equations 18
Darboux transformation for linear systems 3 5 17
Darboux transformation for nonlinear filter equations 18
Darboux transformation for nonlinear Schroedinger equation 3 52
Darboux transformation for nonlocal KdV 69
Darboux transformation for nonstationary Schroedinger equation 16
Darboux transformation for reduced Maxwell — Bloch equations 4 65
Darboux transformation for second harmonic generation equation 67
Darboux transformation for self-induced transparency equation 4 61
Darboux transformation for sine-Gordon equation (SO) 89
Darboux transformation for sine-Gordon equation (SO), nonabelian SO 91
Darboux transformation for Sturm — Liouville equation 78
Darboux transformation for Toda lattice (TL) 4 78 79 82 84
Darboux transformation for Toda lattice (TL), nonabelian TL 87
Darboux transformation for two dimensional (2D) TL 4 78—81 83 89
Darboux transformation for Veselov — Novikov equation 103
Darboux, dressing 33 37 41 47 57 59 64 65 77 79
Darboux, theorem 1 7
Darboux, transformation, inverse 24 25
Davey — Stewartson equation (DS) 4 97 102
Davey — Stewartson equation (DS), extended DS 98
Differential-difference equations 7
Dirac operators 15
Discrete KdV equation 84
Exulton 53 63
Factorization method 26
| Gelfand — Levitan — Marchenko equation 105
Hamiltonian 25 26
Hamiltonian function 104
Hamiltonian interpretation 4 97
Hamiltonian, multidimensional Hamiltonian 25 26
harmonic oscillator 15
Hartree — Fock equation 51
Hermite polynomials 15
Hopf — Kowl ansatz 74
Inverse scattering, method 51
Inverse scattering, transformation 4 77 102
Johnson equation 45 47
Josephson junction 78 88
Jost solution 10—13
Kadomtsev — Petviashvili equation 2 17 30—36 39 40 43 45—47 78 79 81 107
Kaup equation 75
KdV equation 3 4 17 29—36 40—43 47 50 70 104 107
KdV type equation 72
Lax representation 31
Liouville, equation 68
Liouville, formula 3 21
Lump 3 30 35 37
Manakov triad 72
Neumann function 83
Nonabelian version of KdV 88
Nonlinear filter equation 92
Nonlocal KdV equation 68 69
Novikov — Veselov equation 97 102
Phase shift 39 43 57 106 107
Reduced Maxwell — Bloch equation 4 49 59 65
Reflection coefficients 11
Reflectionless potential 3 11
Riemarm problem 30
Schroedinger equation (SE) 1 14—16 21 24 97 104
Schroedinger equation (SE), discrete nonlinear SE 92
Schroedinger equation (SE), discrete nonlinear SE, system, discrete nonlinear 51
Schroedinger equation (SE), matrix SE 25 26
Schroedinger equation (SE), nonlinear SE 4 49 51 53—57 97 102
Schroedinger equation (SE), nonstationary SE 3 16
Schroedinger equation (SE), operator 12—15 38
Schroedinger equation (SE), radial SE 16
Second harmonic equation 67
Self-induced transparency see “SIT”
Silin — Tikhonchuk equation 94
Silin — Tikhonchuk equation, discrete version 94
Sine-Gordon equation (SO) 4 49 61 64 77 78 89 91 104 107
Sine-Gordon equation (SO), nonabelian SO 91
Sinh-Gordon equation 77
SIT see “Self-induced transparency”
SIT equation 4 49 59—62
Sturm — Liouville equation 1 2 7—9 69
Sturm — Liouville problem with Dirichlet boundary conditions 14
Superalgebra 25
Supercharge 25 26
Supersymmetry 24 26
Toda lattice equation (TDL) 4 24 77 104
Toda lattice equation (TDL), nonabelian 77 86
Toda lattice equation (TDL), two dimensional (2D) 4 24 77 91 105 107
Transmission coefficients 11 12
Veselov — Novikov equation 4
Volterra system 84
Zakharov — Shabat method 4 35 105 106
Zakharov — Shabat representation 33 51
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