Modern Group Analysis, Proceedings 10th International Conference, Larnaca, Cyprus, October 24-31, 2004

The 10th International Conference in Modern Group Analysis (MORGAN X)......Page 1
Preface......Page 2
Sponsors......Page 3
Contents......Page 4
1 Introduction......Page 6
3.1 The Group Systematic Formulation......Page 7
3.2 The Invariance Analysis......Page 8
3.4 The Reduction to Ordinary Differential Equation......Page 9
3.5 Analytical Solution......Page 10
4.1 Laplace Equation with Quadratic Boundary Conditions......Page 11
4.2 Poisson Equation with Quartic Boundary Conditions......Page 12
5.1 Laplace Equation with Quartic Boundary Conditions......Page 13
References......Page 14
1 Introduction......Page 15
2 Moser's Solution of the Toda Lattice......Page 18
3 The Toda Lattice is Super-Integrable......Page 20
Acknowledgements......Page 21
1 Introduction......Page 22
2 Inhomogeneously Broadened Model......Page 23
3 Pseudo-Potential Technique......Page 24
4 BÄacklund Transformation......Page 27
5 Solutions......Page 28
6 Discussion of the Solutions......Page 29
7 Summary......Page 30
Acknowledgements......Page 31
1 Introduction......Page 32
2 On the Equivalence Algebra......Page 34
3.1 Case 1......Page 35
3.2 Case 2......Page 36
4 A Remark on the Equivalence Transformations......Page 37
Acknowledgements......Page 38
1 Introduction......Page 39
2 A Position-Dependent Mass Nonlinear Oscillator......Page 40
3 The One-Dimensional Quantum Nonlinear Oscillator......Page 43
4 Periodic Motions and Another Nonlinear Oscillator......Page 44
1 Introduction......Page 47
2 Special Polynomials Associated with Rational Solutions of P......Page 48
3 Rational and Rational-Oscillatory Solutions of the Nonlinear Schrödinger Equation......Page 51
Acknowledgements......Page 55
2 A Modification......Page 58
3.1 Potential Symmetries......Page 60
3.2 Approximate Symmetries......Page 62
4 Conclusion......Page 63
1 Introduction......Page 64
2.1 Main Features......Page 65
2.2 Illustrative Examples......Page 66
3 Applications in Education......Page 68
Acknowledgements......Page 69
2 An Equation in 2+1 Dimensions......Page 71
2.3 The Singular Manifold Method......Page 72
3.1 Dromions......Page 74
3.2 Line Solitons......Page 75
Acknowledgements......Page 76
1 Introduction......Page 77
2 Poisson-Dirac Submanifolds......Page 78
3 Fixed Point Sets of Proper Poisson Actions......Page 81
4 Applications and Further Results......Page 82
1 Introduction......Page 85
2 Lie Symmetries......Page 87
2.1 Classical Potential Symmetries......Page 88
2.2 Nonclassical Potential Symmetries......Page 89
1 Introduction......Page 92
2.1 The Representation of the Solution......Page 95
2.2 Equations of the Ovsyannikov Vortex......Page 96
3 Stationary Solution......Page 98
Acknowledgements......Page 99
1 Introduction......Page 100
2 Linearization by Point Transformations......Page 101
3 Linearization by Contact Transformations......Page 103
4 Examples......Page 105
1 Introduction......Page 107
2 Equivalence Transformations and Choice of Investigated Class......Page 109
3 Local Conservation Laws......Page 111
Acknowledgements......Page 113
1 Introduction......Page 114
2 Applications......Page 115
3 Group-Invariant Solutions Corresponding to the Nonclassical Potential Symmetries......Page 117
Acknowledgements......Page 118
1 Introduction......Page 120
3 The Classical Counterpart......Page 121
4 The Free Heat System......Page 122
6 Euclidean Non-Linear Schrödinger System......Page 123
7 Invariant Polynomials......Page 124
Acknowledgements......Page 125
1 Introduction......Page 126
2 Basic Model: Vlasov{Maxwell Equations......Page 127
3 Expansion of the Plasma Bunch......Page 129
Acknowledgements......Page 132
1 Some Equations of Financial Mathematics......Page 134
1.1 The Black{Scholes Equation......Page 135
1.2 Simpli¯cation of the Black{Scholes Equation......Page 136
1.3 Some Other Equations of Mathematical Finance......Page 137
2 Mean-Variance Hedging......Page 138
3 An Absence of an In¯nite Number of Lie Point Symmetries......Page 139
4 The Classical Connection......Page 140
Acknowledgments......Page 141
1 Introduction......Page 143
3 A Hierarchy of Equations......Page 144
3.1 Quadratic Coefficients......Page 145
4 The Riccati Transformation......Page 147
Acknowledgements......Page 150
2 Bilinear Form of the Camassa{Holm Equation......Page 152
3 Solitary Waves......Page 154
4 Two-soliton solution of the Camassa{Holm equation......Page 155
5 Three-Soliton Solution......Page 156
6 N -Soliton Solutions......Page 157
Acknowledgements......Page 158
1 Introduction......Page 159
2 Self-De°ecting Similarity Solutions for (3)......Page 161
3 Accelerating SFF Solitons......Page 163
4 Equation Classes Having the Accelerating Symmetry......Page 164
1 Introduction......Page 167
2 Admissible Transformations......Page 168
3 Normalized Classes of Di®erential Equations......Page 169
4 Covering Class of Nonlinear SchrÄodinger Equations......Page 170
5 General case of modular nonlinearity with potential......Page 172
Acknowledgements......Page 174
1 Introduction......Page 175
2 Group Classification of the Equation (1)......Page 176
3 Group Classfication of the System (4){(5)......Page 178
5 Discussions of the Group Classifications......Page 179
Acknowledgements......Page 180
1 Introduction......Page 182
2 The Admissible Lie Symmetry Algebra......Page 183
3 The Optimal Systems of Subalgebras......Page 184
Acknowledgements......Page 189
1 Introduction......Page 190
3.1 Centralizer Structure......Page 191
3.3 Adjoint Action and Inner Automorphisms......Page 192
3.4 The Full Automorphism Group......Page 193
4 Discrete Symmetries......Page 195
Acknowledgements......Page 197
1 Introduction......Page 198
2 Form-Preserving Transformations for Generalised Wave Equations......Page 199
4 Differential Invariants......Page 201
5 Linearisation Using Differential Invariants......Page 204
Acknowledgements......Page 205
1 Introduction......Page 207
2 One Class of Partially Invariant Solutions of the Navier{Stokes Equations......Page 208
3 Lie Groups of BÄacklund Transformations......Page 209
Acknowledgements......Page 212
1 Introduction......Page 214
2.2 Burgers Equation with Variable Coe±cients in (2 + 1) Dimensions......Page 215
2.3 KdV Equation with Variable Coe±cients in (2 + 1) Dimensions......Page 218
3 Conclusions......Page 219
Acknowledgements......Page 220
1 Introduction......Page 222
2 Symmetries of Quadrilateral Equations......Page 223
2.2 Symmetries of the Discrete Korteweg{de Vries Equation......Page 226
3 Symmetry Reduction on the Lattice......Page 227
Acknowledgements......Page 229
2 Preliminary Results......Page 231
3 Applications......Page 232
Acknowledgements......Page 235
1 Introduction......Page 236
2 Approximate Symmetry Method......Page 237
3 Group Classi¯cation via Approximate Symmetries......Page 239
4 A Physical Application......Page 241
Acknowledgements......Page 242
1 Introduction......Page 244
2 Derivation of Model Equations Describing a Particulate Trap......Page 245
3 Modelling the Pressure Term......Page 247
4 Group Analysis of Filtration Processes......Page 248
5 Discussion of the Special Cases......Page 249
Acknowledgements......Page 251
1 Introduction......Page 252
2.1 Introduction......Page 253
2.2 Example 1......Page 254
2.3 Example 2......Page 255
3.2 A Particular Solution Employing Resonances......Page 256
4 Equations with Quadratic Sources......Page 257
4.1 Example......Page 258
Acknowledgements......Page 259
List of Participants......Page 260