Two-dimensional nonlinear Schroedinger equation and self-focusing in a two-fluid model of Newtonian cosmological perturbations

Details Two-dimensional nonlinear Schroedinger equation and self-focusing in a two-fluid model of Newtonian cosmological perturbations Two-dimensional nonlinear Schroedinger equation and self-focusing in a two-fluid model of Newtonian cosmological perturbations

Nov 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988a%26a...206....9k&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 206, no. 1, Nov. 1988, p. 9-17.

Astronomy and Astrophysics

Astrophysics

4

Cosmology, Perturbation Theory, Schroedinger Equation, Self Focusing, Two Fluid Models, Astronomical Models, Computerized Simulation, Jeans Theory, Magnetohydrodynamic Stability, Solitary Waves

Scientific paper

The evolution of weakly nonlinear hydrodynamic disturbances on a static cosmological background is studied, emphasizing nonlinear modulational instabilities, solitons, and self-focusing. The model consists of two distinct nonrelativistic fluid components coupled only by gravitation. The two-dimensional nonlinear Schroedinger equation is found to govern the long-term evolution of the envelope of weakly nonlinear, nearly plane-symmetric, almost monochromatic acoustic waves. Nonlinear modulation instability may even arise within a range of wavenumbers for which both modes of the linearized theory are stable, leading to the possibility of soliton formation. The two-fluid system studied here also exhibits a violent nonlinear self-focusing instability of the type observed in experiments with optical beams. Evidence is found for the onset of nonlinear saturation of linear Jeans instabilities.

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