Does the complex deformation of the Riemann equation exhibit shocks?

The Riemann equation u_t + uu_x = 0, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is PT symmetric. A one-parameter PT -invariant complex deformation of this equation, u_t - iu(iu_x)^ε = 0 (ε real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless ε is an odd integer. When ε is an odd integer, the shock-formation time is calculated explicitly.