Burgers Turbulence and the Problem of Star Formation

Star forming molecular clouds are thought to be governed by supersonic, possibly super-Alfvenic turbulence. We introduce a one-dimensional Burgers model with magnetic pressure that explains sustaining of the turbulence on small scales, the turbulent shock fragmentation, and the formation of the universal density statistics,-- features characteristic of the three-dimensional supersonic turbulence. We present an analytical solution for the model and confirm it by direct numerical simulations.