 | Kartashova E. Nonlinear resonance analysis: theory, computation, applications. - Cambridge; New York: Cambridge University Press, 2011. - xv, 223 p.: ill. - Ref.: p.209-220. - Ind.: p.221-223. - ISBN 978-0-521-76360-8
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Preface ........................................................ ix
Glossary ...................................................... xiv
1 Exposition ................................................... 1
1.1 An easy start ........................................... 1
1.2 Two classifications of PDEs ............................ 11
1.3 Hamiltonian formalism .................................. 19
2 Kinematics: Wavenumbers ..................................... 30
2.1 An easy start .......................................... 30
2.2 Irrational dispersion function, analytical results ..... 32
2.3 g-class decomposition .................................. 45
2.4 Rational dispersion function ........................... 57
2.5 General form of dispersion function .................... 60
3 Kinematics: Resonance clusters .............................. 64
3.1 An easy start .......................................... 64
3.2 Topological structure vs dynamical system .............. 66
3.3 Three-wave resonances .................................. 69
3.4 Four-wave resonances ................................... 76
3.5 NR-diagrams ............................................ 82
3.6 What is beyond kinematics? ............................. 88
4 Dynamics .................................................... 90
4.1 An easy start .......................................... 90
4.2 Decay instability ...................................... 93
4.3 A triad ................................................ 96
4.4 Clusters of triads .................................... 106
4.5 A quartet ............................................. 116
4.6 Explosive instability ................................. 117
4.7 NR-reduced numerical models ........................... 122
4.8 What is beyond dynamics? .............................. 127
5 Mechanical playthings ...................................... 130
5.1 Linear pendulum ....................................... 130
5.2 Elastic pendulum ...................................... 138
6 Wave turbulent regimes ..................................... 144
6.1 An easy start ......................................... 144
6.2 Quasi-resonances vs approximate interactions .......... 147
6.3 Model of laminated turbulence ......................... 150
6.4 Energy cascades: dynamic vs kinetic ................... 158
6.5 Rotational capillary waves ............................ 161
6.6 Discrete regimes in various wave systems .............. 170
6.7 Open problems ......................................... 176
7 Epilogue ................................................... 182
Appendix Software ............................................. 185
References .................................................... 209
Index ......................................................... 221
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