  The nonlinear Schr\"{o}dinger equation with variable coefficients has
applications in numerous areas of physics,specifically in the context of
nonlinear optics and Bose-Einstein condensate. Apart from the usual bright and
dark-soliton solutions, the so-called rational soliton solutions are perceived
to have tremendous impact in futuristic applications and understanding many
natural phenomena. In this work, we have studied various orders of rational
solution of the variable coefficient nonlinear Schr\"{o}dinger equation. It is
possible to extract the first and the second-order controlled KM-like breather
by periodic modulation of the dispersion along the propagation direction. The
amplitude of the dispersion modulation controls the background as well as the
breather peak power in the case of the first-order rational soliton solution,
whereas the spatial frequency controls the breathing frequency of the KM-like
breather. Our study reveals that it is possible to obtain various new features
in the third order rational soliton by modulating the dispersion parameter.
