  In this work, we develop a theory of (meta)stable states of N\'eel-type
skyrmions in weak nonuniform magnetic fields. We claim an Ansatz for modeling
the non-symmetric magnetization that can be implied for both analytics and
numerical simulations. Our theory accounts for changes in the size of skyrmion
parameters and also includes deformations from the centrally symmetric shape.
The ansatz streamlines the analytic calculation of the skyrmion free energy,
enhancing the efficiency of the minimizing process. Performing the minimization
in two stages, one can find all the minima, global and local, of the free
energy, discovering the stable and metastable states. We apply the developed
methodology to investigate the (meta)stable configurations of skyrmions
influenced by the stray field of a Pearl vortex. Our study reveals the
dependence of skyrmion spatial parameters on the vortex field effective
strength and presents a phase diagram identifying regions where metastable
configurations are predicted. Corroborated by micromagnetic simulations, our
findings offer a detailed perspective on the interaction between magnetic
skyrmions and superconducting vortices.
