Multiple-scales method for nonlinear wave modulation

Details Multiple-scales method for nonlinear wave modulation Multiple-scales method for nonlinear wave modulation

Sep 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989ap%26ss.159..347e&link_type=abstract

Astrophysics and Space Science (ISSN 0004-640X), vol. 159, no. 2, Sept. 1989, p. 347-350.

Astronomy and Astrophysics

Astrophysics

1

Electron Plasma, Perturbation Theory, Plane Waves, Schroedinger Equation, Electron Density (Concentration), Nonlinear Equations, Partial Differential Equations, Wave Interaction

Scientific paper

A nonlinear Schroedinger equation describing the nonlinear modulation of a monochromatic plane plasma wave is derived using a multiple-scales perturbation theory. This equation differs from that obtained by Nayfeh (1965) for the same problem with the same technique, but agrees with that obtained by Kakutani and Sugimoto (1974) using the Krylov-Bogoliubov-Mitropolsky method. An adiabatic model is considered of one-dimensional electron plasma waves in a warm electron plasma where ions are immobile and form a uniform positive background. The analysis takes into account the dispersion effect, and the derived equation shows that the amplitude variation of a monochromatic plane wave is controlled by the dispersion term, the linear term, and the nonlinear interaction terms.

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