Nonlinear wave propagation in collisionless finitebeta inhomogeneous plasmas
Abstract
Four coupled nonlinear evolution equations for the electrostatic potential, the density fluctuation, and the two vector potentials are derived from the twofluid and Maxwell's equations that describe lowfrequency collisionless finitebeta inhomogeneous plasmas. Under the assumption of weak turbulence, the above equations reduce to the nonlinear Schrödinger equation. The technique adopted here is considered as an extension of the formal KarpmanKrushkal [Sov. Phys. JETP 28, 277 (1969)] method to a system of nonlinear partial differential equations. The general exact traveling wave solution to the nonlinear Schrödinger equation is obtained with the help of the HamiltonJacobi theory. This general solution may be regarded as describing a final nonlinear stage of the modulational instability. It is also shown that a solitary wave solution to the nonlinear Schrödinger equation, which corresponds to the limiting case of the general solution, is given by means of the simple iterative method.
 Publication:

Physics of Fluids
 Pub Date:
 August 1988
 DOI:
 10.1063/1.866625
 Bibcode:
 1988PhFl...31.2233K
 Keywords:

 Collisionless Plasmas;
 Nonlinear Evolution Equations;
 Nonuniform Plasmas;
 Plasma Potentials;
 PlasmaElectromagnetic Interaction;
 Wave Propagation;
 Electric Potential;
 Maxwell Equation;
 Schroedinger Equation;
 Solitary Waves;
 Traveling Waves;
 Plasma Physics