Riemann’s Wavesin Chaplygin Gas
We have investigated propagation of Riemann waves in an ideal ﬂuid with negative pressure, the so-called Chaplygin gas. We consider barotropic motion of the medium when the pressure is P = P( ρ) in the assumption u = u( ρ), where u — the velocity, ρ — density of the medium. The system of hydrodynamic equations then reduces to a wave equation of the ﬁrst order, which describes a wave with variable speed. It is shown that these waves have deformed proﬁle, which leads to an ambiguous deﬁnition of ρ. In order to remove this lack in the original equation we have introduced a member with the second derivative, which leads to the appearance of waves with a stationary proﬁle which is a rarefaction wave.