Abstract
Nonlinear wave modulation associated with the gravitational stability of an infinite homogeneous gas is investigated by the reductive perturbation method. It is shown that the weakly nonlinear wave with the carrier wave number more than the Jeans wave number kJ is governed by a nonlinear Schrödinger (NLS) equation. That NLS equation changes its type from modulationally unstable one to stable one across a critical wave number kc (> kJ). Further it is shown that the weakly nonlinear wave near the marginal state of instability, i.e., near kJ, obeys an unstable NLS equation. From these results, it is conjectured that the nonlinearity may lead to various types of envelope soliton formations in a self-gravitating medium.
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