Prog. Theor. Phys. Vol. 95 No. 1 (1996) pp. 51-63
Nonlinear Self-Modulation in Newtonian Gravity
Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-01
*Department of Fundamental Sciences, FIHS, Kyoto University, Kyoto 606-01
(Received September 1, 1995)
We study quasi-nonlinear evolution of the density perturbation in Newtonian gravity. Weak mode-mode coupling in a small range below the Jeans wavelength is considered. In order to extract nonlinear dynamics we utilize a reductive perturbation, which is well known in mechanics and hydrodynamics and improves a naive perturbation. We show that the basic equations for the acoustic wave reduce to a nonlinear Schrödinger equation. It describes a competition between dispersion originated from gravitational attraction and nonlinearity up to cubic order of the amplitude of the acoustic wave. In purely 1-dimensional motion, there exists localized structures as soliton solutions of two distinctive types depending on the wavelength. More interesting is an instability present in 3-dimensional motion. Namely, a progressive wave is unstable under a long-wave perturbation transverse to the direction of progression. It may imply a possible nonlinear growth of the density fluctuation below the Jeans scale.
DOI : 10.1143/PTP.95.51
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