On propagation of 2D nonlinear density waves
Two-dimensional nonlinear density waves in a large-scale infinitesimal gaseous medium with neglected selfgravity are considered. In terms of the radially expanding features in the central disc of the Galaxy a reduced model of axially symmetric density perturbations in a rotating disc is investigated. Analytical estimations on the amplitude decay rate are obtained, while integrating the governing hydrodynamical PDEs along the characteristic curves. For nonsymmetric 2D propagation, we propose a modified method of characteristics as an adaptive mesh approach that incorporates straightforward treatment of the most critical integration regions, such as of discontinuities and shock fronts.