We study the dynamics of vortices in an inhomogeneous Gross-Pitaevskii equation i∂tu = Δu + 1/ϵ2 (ρ2 ϵ (x) - |u|2). For a unique scaling regime |ρϵ(x) - 1| = O(log ϵ-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.
Bibliographical noteFunding Information:
The work of the second author was supported in part by NSF applied math grant DMS-1312874 and NSF CAREER grant DMS-1352353. The work of the third author was supported in part by NSF CAREER grant DMS-0955687 and NSF grant DMS-1516565.
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- Critical scaling