Burgers turbulence is the study of Burgers equation with random initial data or forcing. The problem is to understand the statistics of shocks and their interaction.
We derive kinetic equations that describe the process of shock clustering for any scalar conservation law with convex flux (in particular, Burgers equation) and a large class of random initial data. These equations have the structure of a Lax pair, and several features that are strongly reminiscent of complete integrability.