  We study photoinduced dynamics triggered by an inhomogeneity due to
competition between charge density waves (CDWs) and superconductivity. As a
simple example, we consider the superconducting (SC) interface between two CDW
domains with opposite signs. The real-time dynamics are calculated within the
time-dependent Hartree--Fock--Bogoliubov framework, where the order parameter
dynamics and the nonequilibrium quasiparticle distribution functions are
studied. We also calculate the various dynamical response functions within a
generalized random phase approximation. Through comparisons between the real
time dynamics and the analysis of the response functions, it is found that the
photo-driven SC interface can emit collective modes of the SC order parameter.
This is analogous to the spin wave emission from the magnetic domain wall in an
antiferromagnet, particularly in the case of a low driving frequency, where the
order parameters can be mapped onto the pseudospin picture. In the
high-frequency case, we find a domain wall melting caused by changes in the
quasiparticle distribution, which induces superconductivity in the whole
system.
