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 <i>P </i>= <i>P</i>( <i>ρ</i>) in the assumption <i>u </i>= <i>u</i>( <i>ρ</i>), where <i>u </i>— the velocity, <i>ρ </i>— 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 <i>ρ</i>. 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.