Abstract
Nonlinear wave modulation associated with the gravitational stability of an infinite homogene ous gas is investigated by tbe reductive perturbation method. It is shown that the weakly nonlinear wave with the carrier wave number more than the Jeans wave number k, is governed by a nonlinear Schrodinger (NLS) equation. That NLS equation changes its type from modulationally unstable one to stable one across a critical wave number kc ( > k, ). Further it is shown that the weakly nonlinear wave near the marginal state of instability, i. e., near k1 , obeys an unstable NLS equation. From these results, it is conjectured that tbe nonlinearity may lead to various types of envelope soliton formations in a self-gravitating medium.
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