  As shown in recent experiments [Auslaender et al., Nature Physics 5, 35
(2009)] magnetic force microscopy permits one not only to image but also to
manipulate an individual vortex in type-II superconductors, and this
manipulation provides a new powerful tool to study vortex dynamics and pinning.
We derive equations that describe the deformation of an individual vortex in an
anisotropic biaxial type-II superconductor under the action of the microscope's
magnetic tip. These equations take into account the driving force generated by
the tip, the elastic force caused by the vortex deformation, and the pinning
force exerted by point defects. Using these equations, we reproduce the main
features of the experimental data obtained by Auslaender et al.
