SOLITON FORMATION IN A SELF-GRAVITATING GAS

Nonlinear wave modulation associated with the gravitational stability of an infinite homogeneous gas is investigated by the reductive pertur bation method. It is shown that the weakly nonlinear wave with the car rier wave number more than the Jeans wave number k(J) is governed by a nonlinear Schrodinger (NLS) equation. That NLS equation changes its t ype from modulationally unstable one to stable one across a critical w ave number k(c) (>k(J)). Further it is shown that the weakly nonlinear wave near the marginal state of instability, i.e., near k(J), obeys a n unstable NLS equation. From these results, it is conjectured that th e nonlinearity may lead to various types of envelope soliton formation s in a self-gravitating medium.