  We discuss two complementary problems: adiabatic loading of one-dimensional
bosons into an optical lattice and merging two one-dimensional Bose systems.
Both problems can be mapped to the sine-Gordon model. This mapping allows us to
find power-law scalings for the number of excitations with the ramping rate in
the regime where the conventional linear response approach fails. We show that
the exponent of this power law is sensitive to the interaction strength. In
particular, the response is larger, or less adiabatic, for strongly (weakly)
interacting bosons for the loading (merging) problem. Our results illustrate
that in general the nonlinear response to slow relevant perturbations can be a
powerful tool for characterizing properties of interacting systems.
