Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0613.76129
Goldman, Martin V.
Langmuir wave solitons and spatial collapse in plasma physics. (English)
[J] Physica D 18, 67-76 (1986). ISSN 0167-2789

This paper deals with coherent structures associated with Langmuir waves (longitudinal waves of electric field oscillating near the plasma frequency). In the 1-D adiabatic and Hamiltonian limit, the envelope of such waves obeys a simple cubic nonlinear Schrödinger (NLS) equation which possesses an exact (inverse scatter) solution. The marked changes in the properties of the nonlinear entities (solitons and breathers) were stressed in this paper. \par In particular, the author discussed recent numerical and analytic results concerning: the effect on the 1-D cubic NLS equation, of introducing Landau damping at short scales and externally-driven instability at long scales; new results concerning self-similar solutions to the NLS equation in two dimensions; and a new mechanism for transfer of wave energy from long to short scales by wave-packet nucleation in density cavities, described by the Zaharov equations (the non-adiabatic generation of the NLS equations).
[Lung Yu Shih]

MSC 2000:: *76X05 Plasmic flows
35Q99 PDE of mathematical physics and other areas

Keywords: nonlinear Schrödinger equation; self-similar solutions; Zaharov equations; exact solution; coherent structures; Langmuir waves; Hamiltonian limit; solitons; Landau damping; externally-driven instability; transfer of wave energy; wave-packet nucleation; density cavities; non-adiabatic generation

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]