<p>Recently, two of the present authors showed that even when the axion momentum is much smaller than its mass, the axion can still behave like radiation if its energy density greatly exceeds the maximum potential energy set by the cosine-type potential. In the relevant regime, even if the axions are particles in the initial conditions with large phase-space occupation numbers, their dynamics are described by a classical field (wave) that effectively averages over the periodic potential. As the energy density redshifts down to the scale of the potential, a nonlinear transition occurs, during which the axion’s adiabatic invariant is not conserved because of the formation of layers of domain walls. In this paper, we revisit the analysis of axion dark matter by incorporating the effects of this nonlinear transition through a precise study of the axion spectrum. We demonstrate that in the parameter region with a relatively small decay constant — often favored in axion search experiments — special care is required when estimating the axion abundance and spectrum. We also highlight a scenario in which axions are produced through the stimulated decay of a modulus, where the nonlinear transition occurs. Furthermore, we discuss related phenomena, including QCD axion dark matter, the formation of axion clumps such as miniclusters and axion stars, gravitational wave production, and primordial blackholes as dark matter.</p>