Introduction to Nonlinear Fluid-Plasma Waves

I. Introduction.- II. Nonlinear oscillations in an electron plasma.- III. Nonlinear ion-acoustic waves.- (i) Shockwaves.- (ii) Solitary waves.- (iii) Interacting solitary waves.- (iv) Ion-acoustic waves in a magnetized plasma.- IV. Parametric excitations of plasma waves.- (i) Parametric excitation of electromagnetic waves by an oscillating electric field.- (ii) Wave-wave interactions.- (a) Nonlinear resonant interactions between two electromagnetic waves and a Langmuir wave.- (b) Nonlinear resonant interactions between two transverse electromagnetic waves and an ion-acoustic wave.- (c) Nonlinear resonant interactions between two circularly-polarized waves and a Langmuir wave.- (d) Nonlinear resonant interactions between three extraordinary waves.- (e) Stimulated wave-scattering phenomena.- (f) Oscillating two-stream instability.- (g) The question of the time-dependent ponderomotive force.- V. Modulational instability and envelope solitons.- (i) Langmuir solitons.- (a) Instability and collapse of Langmuir solitons.- (b) Nearly sonic Langmuir solitons.- (c) Effect of finite spectral-width on the modulational instability of Langmuir waves.- (d) Strong Langmuir turbulence.- (ii) Modulational stability of ion-acoustic waves.- (iii) Upper-hybrid solitons.- (a) Subsonic and supersonic upper-hybrid solitons.- (b) Sonic upper-hybrid solitons.- (c) Upper-hybrid solitons in an electron plasma.- (iv) Lower-hybrid solitons.- (v) Whistler solitons.- VI. Nonlinear relativistic waves.- (i) A coupled system of an electromagnetic wave and a Langmuir wave.- (a) Purely transverse waves.- (b) Luminous waves.- (c) A perturbation theory for the general coupled system.- (ii) Nonlinear relativistic waves in a magnetized plasma.- (a) Purely transverse waves.- (b) Waves with ? ? 1.- (iii) Relativistic modulational instability of an electromagnetic wave.- VII. Nonlinear waves in an inhomogeneous plasma.- (i) Ion-acoustic solitary waves in an inhomogeneous plasma.- Appendix 1: The fluid model for a plasma.- Appendix 2: Review of linear waves.- (i) Plasma oscillations.- (ii) Ion-acoustic waves.- (iii) Waves in a magnetized plasma.- (a) Propagation along the magnetic field.- (b) Propagation transverse to the magnetic field.- References.