5 citations · 5 across the 3 of their papers we have counts for
4 papers
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…
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…
A review on asymptotic stability of solitary waves in nonlinear dispersive problems in dimension one
Pierre Germain
We review asymptotic stability of solitary waves for nonlinear dispersive equations set on the line. Our focus is threefold: first, the nonlinear Schrodinger equation; second, the…
Energy estimates in sum-product and convexity problems
Akshat Mudgal
We prove a new class of low-energy decompositions which, amongst other consequences, imply that any finite set of integers may be written as , where and a…