Velocity characteristic and stability of wave solutions for a candle reactor with thermal feedback

•We study CANDLE, the stationary nuclear fission wave, its velocity and stability.•Presented model of a U-Pu fuelled reactor includes β-decays and thermal feedback.•At specified values of reactor parameters, two waves of different velocities exist.•The lower velocity solution is unstable; no real waves of such velocities exist.•The revealed effects are important at heat power densities of practical interest.