  Nambu-Goldstone modes associated with (topological) defects such as vortices
and domain walls in (super)fluids are known to possess quadratic/non-integer
dispersion relations in finite/infinite-size systems. Here, we report
interpolating formulas connecting the dispersion relations in finite- and
infinite-size systems for Kelvin modes along a quantum vortex and ripplons on a
domain wall in superfluids. Our method can provide not only the dispersion
relations but also the explicit forms of quasiparticle wavefunctions $(u,v)$.
We find a complete agreement between the analytical formulas and numerical
simulations. All these formulas are derived in a fully analytical way, and
hence not empirical ones. We also discuss common structures in the derivation
of these formulas and speculate on the general procedure.
