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math.AP2025
Absence of embedded spectrum for nonlinear Schrödinger equations linearized around one dimensional ground states
Charles Collot, Pierre Germain, Eliot Pacherie
We consider the nonlinear Schrödinger equation in dimension one for a generic nonlinearity. We show that ground states do not have embedded eigenvalues in the essential spectrum of…
math.AP2025
Estimates for the Gross-Pitaevskii equation linearized around a vortex
Charles Collot, Pierre Germain, Eliot Pacherie
We consider the linearized two-dimensional Gross-Pitaevskii equation around a vortex of degree one, with data in the same equivariance class. Various estimates are proved for the s…