| Nonlinear Phenomena Involving Dispersive Alfvén Waves | p. 1 |
| Introduction | p. 1 |
| Dispersive Alfvén waves in a uniform plasma | p. 3 |
| Generation of Alfvén waves | p. 5 |
| Nonlinear effects caused by inertial Alfvén waves | p. 10 |
| Amplitude modulation of kinetic Alfvén waves | p. 14 |
| Modulation of EMICA waves | p. 16 |
| Self-interaction between dispersive Alfvén waves in nonuniform plasmas | p. 18 |
| Chaos in Alfvénic turbulence | p. 24 |
| Summary and conclusions | p. 26 |
| References | p. 28 |
| Whistler Solitons, Their Radiation and the Self-Focusing of Whistler Wave Beams | p. 31 |
| Introduction | p. 31 |
| Basic equations. Slab ducts | p. 32 |
| Full wave solutions for the slab ducts | p. 37 |
| Slabwhistlersolitons | p. 41 |
| Self-focusing of whistler wave beams | p. 44 |
| Concluding remarks | p. 51 |
| References | p. 52 |
| Alfvén Wave Filamentation and Plasma Heating | p. 54 |
| Introduction | p. 54 |
| Filamentation of dispersive Alfvén waves | p. 56 |
| Filamentation of weakly dispersive wave trains | p. 64 |
| Filamentation in the weakly dispersive longwavelength regime | p. 74 |
| Conclusions | p. 80 |
| References | p. 81 |
| Nonlinear Quasiresonant Alfvén Oscillations in a One-Dimensional Magnetic Cavity | p. 83 |
| Introduction | p. 83 |
| Basic equations and assumptions | p. 84 |
| Derivation of the governing equations | p. 87 |
| Energetics | p. 90 |
| Multistability | p. 91 |
| Solutions with shocks and high-Reynolds-number bifurcations | p. 98 |
| Conclusions | p. 101 |
| References | p. 102 |
| On the Reflection of Alfvén Waves in the Inhomogeneous Solar Wind | p. 104 |
| Introduction | p. 104 |
| Effects of stratification, Hall currents, non-uniform magnetic fields and mean flow | p. 107 |
| Models combining radial stratification, mean flow and monopole external magnetic field | p. 132 |
| References | p. 156 |
| Relativistic Alfvén Solitons and Acceleration of Cosmic Rays | p. 160 |
| Introduction | p. 160 |
| The nonlinear relativistic wavefront | p. 161 |
| Generation of a parallel electric field | p. 166 |
| Electron-positron plasma | p. 168 |
| Relativistic Fermi acceleration | p. 169 |
| Astrophysics consequences and head on collision of solitons | p. 174 |
| Cosmic rays scattering off magnetic disturbances | p. 176 |
| Conclusion | p. 179 |
| References | p. 180 |
| Reduced Models of Magnetohydrodynamic Turbulence in the Interstellar Medium and the Solar Wind | p. 182 |
| Introduction | p. 182 |
| The four-field model | p. 185 |
| The NI-MHD model | p. 188 |
| Four-field simulations: implications for pressure fluctuations | p. 190 |
| Anisotropic spectra in weak turbulence theory | p. 192 |
| References | p. 196 |
| Alfvénic Turbulence and Wave Propagation in the Corona and Heliosphere | p. 198 |
| Alfvén waves observed in the solar wind | p. 198 |
| Basic features of linear propagation | p. 199 |
| Observations of Alfvén wave generation | p. 204 |
| Non-linear propagation in the lower atmosphere: Parametric decay and filamentation | p. 208 |
| Alfvén solitons in the solar wind | p. 215 |
| Conclusions | p. 220 |
| References | p. 221 |
| Nonlinear Alfvén Wave Interaction with Large-Scale Heliospheric Current Sheet | p. 222 |
| Introduction | p. 222 |
| A model for Alfvén wave interaction with heliospheric current sheet | p. 225 |
| Numerical results | p. 230 |
| The effects of an inhomogeneous entropy distribution | p. 238 |
| Discussionandconclusions | p. 245 |
| References | p. 248 |
| Coherent Electrostatic Nonlinear Waves in Collisionless Space Plasmas | p. 251 |
| Introduction | p. 251 |
| Coherent ion acoustic waves in the solar wind | p. 252 |
| Review of the observational evidence on coherent waves in the Earth's environment | p. 258 |
| Theoretical interpretations | p. 263 |
| Conclusion | p. 265 |
| References | p. 265 |
| Modeling the Dissipation Range of Magnetofluid Turbulence | p. 269 |
| Observational background | p. 269 |
| More realistic dissipation operators | p. 276 |
| Summary and conclusions | p. 286 |
| References | p. 287 |
| A Weak Turbulence Theory for Incompressible MHD | p. 291 |
| Introduction and general discussion | p. 291 |
| The derivation of the kinetic equations | p. 298 |
| General properties of the kinetic equations | p. 304 |
| Asymptotic solution of the 3D kinetic equations | p. 308 |
| Two-dimensional problem | p. 308 |
| Front propagation | p. 318 |
| Nonlocal isotropic 3D MHD turbulence | p. 323 |
| Conclusion | p. 324 |
| References | p. 328 |
| Shell Models for MHD Turbulence | p. 331 |
| Introduction | p. 331 |
| Models with nearest neighbour interactions | p. 332 |
| Models with nearest and next-nearest interactions | p. 333 |
| Dynamo action in MHD shell models | p. 335 |
| Spectral properties in stationary forced state | p. 338 |
| Fluxes, inertial range and intermittency | p. 339 |
| Conclusions | p. 343 |
| References | p. 344 |
| Dynamics of Vortex and Magnetic Lines in Ideal Hydrodynamics and MHD | p. 346 |
| Introduction | p. 346 |
| General remarks | p. 349 |
| Vortex line representation | p. 353 |
| Variational principle | p. 356 |
| Integrable hydrodynamics | p. 357 |
| Lagrangian description of MHD | p. 359 |
| Frozen-in MHD fields | p. 361 |
| Relabeling symmetry in MHD | p. 364 |
| Variational principle for incompressible MHD | p. 366 |
| References | p. 367 |
| Quasi-Two-Dimensional Hydrodynamics and Interaction of Vortex Tubes | p. 369 |
| Introduction | p. 369 |
| Quasi-two-dimensional hydrodynamics | p. 370 |
| Dynamics of the isolated vortex tube | p. 373 |
| Vortex tube in an external flow | p. 378 |
| Interaction of vortex tubes | p. 380 |
| Instability and collapse of traveling vortex pair | p. 381 |
| Solitons on the co-rotating vortex pair | p. 383 |
| References | p. 385 |
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