  Induced Compton scattering (ICS) is an interaction between intense
electro-magnetic radiations and plasmas, where ICS transfers the energy from
photons to plasmas. Although ICS is important for laser plasma interactions in
laboratory experiments and for radio emission from pulsars propagating in
pulsar wind plasmas, the detail of photon cooling process has not been
understood. The problem is that, when ICS dominates, evolution of photon
spectra is described as a nonlinear convection equation, which makes photon
spectra to be multi-valued. Here, we propose a new approach to treat evolution
of photon spectra affected by ICS. Starting from the higher-order Kompaneets
equation, we find a new equation that resolves the unphysical behavior of
photon spectra. In addition, we find the steady-state analytic solution, which
is linearly stable. We also successfully simulate the evolution of photon
spectra without artificial viscosity. We find that photons rapidly lose their
energy by ICS with continuously forming solitary structures in frequency-space.
The solitary structures have the logarithmically same width characterized by an
electron temperature. The energy transfer from photons to plasma is more
effective for broader spectrum of photons such as expected in astrophysical
situations.
