Propagation of nonlinear waves in a rarefied bubbly flow

The one-dimension Russo--Smereka kinetic equation describing the propagation of nonlinear concentration waves in a rarefied bubbly fluid is considered. Reductions of the model to finite component systems are derived. Stability of the bubbly flow in terms of hyperbolicity of the kinetic equation is studied. Conservation form of the model is proposed and numerical solution of the Cauchy problem with discontinuous initial data is obtained.