  We study dynamics of a superconducting condensate in the presence of a domain
wall defect in the order parameter. We find that broken translation and
reflection symmetries result in new collective excitations, bound to the domain
wall region. Two additional amplitude/Higgs modes lie below the bulk
pairbreaking edge $2\Delta$; one of them is a Goldstone mode with vanishing
excitation energy. Spectrum of bound collective modes is related to the
topological structure and stability of the domain wall. The `unbound' bulk
collective modes and transverse gauge field mostly propagate across the domain
wall, but the longitudinal component of the gauge field is completely
reflected. Softening of the amplitude mode suggests reduced damping and
possible route to its detection in geometrically confined superfluids or in
superconductor-ferromagnetic heterostructures.
