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Self‐Modulation and Envelope Solitons of Spiral Density Waves
Author(s) -
Meinel R.
Publication year - 1983
Publication title -
astronomische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.394
H-Index - 63
eISSN - 1521-3994
pISSN - 0004-6337
DOI - 10.1002/asna.2113040203
Subject(s) - physics , envelope (radar) , polytropic process , modulation (music) , nonlinear system , density wave theory , nonlinear schrödinger equation , plane wave , classical mechanics , quantum electrodynamics , spiral (railway) , mechanics , quantum mechanics , astrophysics , mathematical analysis , mathematics , telecommunications , radar , computer science , acoustics
A nonlinear evolution equation describing the modulation of the L IN ‐S HU density waves in the tight winding approximation is discussed. A fluid dynamical model with a polytropic relationship between the pressure and the density is used. The equilibrium state is assumed to be homogeneous in the considered radial range. As in the case of plane density waves (I KEUCHI and N AKAMURA 1976) the modulation of spiral density waves is governed by the nonlinear S CHRödinger equation. For large wave numbers the process of self‐modulation generates envelope solitons and could explain the permanent renewal of the spiral design of galaxies.