N-soliton pattern in a self-gravitating fluid disk

Physics

Scientific paper

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Celestial Mechanics, Mechanical Properties Of Liquids

Scientific paper

A nonlinear process of density perturbations in an infinitesimally thin fluid disk with uniform rotation and self-gravitation is investigated. In a locally Cartesian system the amplitude equation turns out to be the nonlinear Schrödinger equation. By solving the equation it is shown that the perturbed density can undergo modulation in space, forming an N-soliton pattern in the radial direction. An astrophysical application of this model to the early evolution of Saturn's ring system is studied.

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