Nonlinear waves in an ultra-relativistic heat-conducting fluid I (Landau-Lifshitz formulation)

A second-order theory for relativistic heat-conducting fluids in Landau-Lifshitz scheme is formulated. Weak discontinuity waves propagation is also investigated and the expression for the velocities of propagation of hydrodynamic and heat waves for an ultra-relativistic fluid is obtained. Moreover, the evolution equations for the amplitude of the above discontmuities are derived and the behaviour at the wave fronts is discussed.