Gross-Pitaevskii vortex motion with critically scaled inhomogeneities - Kurzke, Matthias; Marzuola, Jeremy L.; Spirn, Daniel (Society for Industrial and Applied Mathematics, 2017)
We study the dynamics of vortices in an inhomogeneous Gross--Pitaevskii equation iδtu = Δu + 1/ε²(ρ² ε(ᵡ) - |u|²). For a unique scaling regime |ρε(ᵡ) - 1 = O(logε¯¹), it is shown that vortices can interact both with the background perturbation and with each other. Results for associated parabolic and elliptic problems are discussed.