Abstract
In this paper, weakly nonlinear dynamics of spiral galaxies is studied, using reductive perturbation method. One primarily aims at the derivation of possible soliton solution for two dimensional geometry, in the state of marginal stability. In order to use proper coordinate transformation, it was necessary to analyze stability of the linearized system of equations, and to define proper parameter regime. Such parameter regime is in agreement with the observational data, too. The influence of finite-thickness of the galaxy disk on dispersive properties of the system is studied, extending approximate solution of Poisson?s equation. For both cases, infinitesimally thin disk and disk of finite thickness, the same type of NLS equation is derived, but with different coefficients for nonlinear and dispersive terms. This means that corresponding soliton solutions have different properties. By comparing soliton properties with observational data it is possible to control validity of approximation for different geometry of the model.
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