Resonantly interacting non-linear waves in a van der Waals gas

The present paper uses the method of multiple time scales to derive the asymptotic solution of system of one-dimensional quasilinear hyperbolic equations for the generalized geometry in van der Waals gas. The transport equation for the amplitude of resonantly interacting high frequency waves propagating into non-ideal gas is derived. Further, we discuss the cases when the initial data for the wave amplitude is of 2π periodicity. The evolutionary behavior of non-resonant wave modes culminating into shock wave and its location are examined in van der Waals fluid.