  We construct breather and rogue wave solutions of a variable coefficient
nonlinear Schr\"odinger equation with an external linear potential. This
generalized model describes the nonlinear wave propagation in an inhomogeneous
plasma/medium. We derive several localized solutions including Ma breather,
Akhmediev breather, two-breather and rogue wave solutions of this model and
show how the inhomogeneity of space modifies the shape and orientation of these
localized structures. We also depict the trajectories of the inhomogeneous
rogue wave. Our results may be useful for controlling plasmonic energy along
the plasma surface.
