The flow induced by the propagation of a detonation wave in an axisymmetric channel is considered. Dependencies of average impulse and average specific impulse on lateral wall form are investigated for the stage up to the moment when the detonation wave exits the channel. For the asymptotic self-similar solution in the case of a conic wall, the cone apex angle corresponding to the average impulse maximum has been found. In another not self-similar case, numerical simulations based on the Godunov method have been performed for the class of parabolic walls. Walls that maximize average impulse and average specific impulse have been found. The problem can be considered as a model of pulse detonation engine operating cycle, which gives an estimation of its maximum possible thrust characteristics.