Nonlinear wave propagation in collisionless finite-beta inhomogeneous plasmas

Journal Article · Mon Aug 01 04:00:00 EDT 1988 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.866625· OSTI ID:7055856

Katou, K; Weiland, J

Four coupled nonlinear evolution equations for the electrostatic potential, the density fluctuation, and the two vector potentials are derived from the two-fluid and Maxwell's equations that describe low-frequency collisionless finite-beta inhomogeneous plasmas. Under the assumption of weak turbulence, the above equations reduce to the nonlinear Schroedinger equation. The technique adopted here is considered as an extension of the formal Karpman--Krushkal (Sov. Phys. JETP 28, 277 (1969)) method to a system of nonlinear partial differential equations. The general exact traveling wave solution to the nonlinear Schroedinger equation is obtained with the help of the Hamilton--Jacobi 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 Schroedinger equation, which corresponds to the limiting case of the general solution, is given by means of the simple iterative method.

• Research Organization: Institute of Electromagnetic Field Theory, Chalmers University of Technology, S-412 96 Goeteborg, Sweden
• OSTI ID: 7055856
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 31:8; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700108* -- Fusion Energy-- Plasma Research-- Wave Phenomena
BETA RATIO
COLLISIONLESS PLASMA
COULOMB FIELD
DIFFERENTIAL EQUATIONS
DISPERSION RELATIONS
ELECTRIC FIELDS
EQUATIONS
FLUCTUATIONS
HAMILTON-JACOBI EQUATIONS
INHOMOGENEOUS PLASMA
MAGNETIZATION
MAXWELL EQUATIONS
NONLINEAR PROBLEMS
PARTIAL DIFFERENTIAL EQUATIONS
PLASMA
PLASMA DENSITY
POTENTIALS
SCHROEDINGER EQUATION
TRAVELLING WAVES
TURBULENCE
VARIATIONS
WAVE EQUATIONS
WAVE PROPAGATION