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The spinning gas clouds with precession: the symmetry generators. (English) Zbl 1382.76212
Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 13th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 3–8, 2011. Sofia: Bulgarian Academy of Sciences. Geometry, Integrability and Quantization, 114-131 (2012).
Summary: The Dyson model of a spinning ellipsoidal gas cloud expanding into a vacuum has been found to be Liouville integrable under certain additional assumptions, such as the absence of either vorticity or of angular momentum. Here we present a new formulation in the form of a $$4\times 4$$ matrix equation, which generalizes a similar result obtained in rotationless cases. This implies to consider an extended affine space of seven dimensions, in which the seven coordinates of the point-mass representative of the cloud obey differential equations of the same general form as those defining the elliptic functions. This leads very directly to the linearization of the system in the so-called degenerate cases. We obtain also explicit expressions for the symmetry generators, a prerequisite in the task of constructing a Backlund transformation.
For the entire collection see [Zbl 1245.00048].
##### MSC:
 76N15 Gas dynamics (general theory) 58J72 Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds
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