Painlevé analysis and transformations for a generalized two-dimensional variable-coefficient Burgers model from fluid mechanics, acoustics and cosmic-ray astrophysics

摘要

Generalized two-dimensional variable-coefficient Burgers model is of current value in fluid mechanics, acoustics and cosmic-ray astrophysics. In this paper, Painlevé analysis leads to the constraints on the variable coefficients for such a model to pass the Painlevé test and to an auto-B?cklund transformation. Moreover, four transformations from this model are constructed, to the standard two-dimensional and one-dimensional Burgers models with the relevant constraints on the variable coefficients via symbolic computation. By virtue of the given transformations the properties and solutions of this model can be obtained from those of the standard two-dimensional and one-dimensional ones.