David Chiron, Eliot Pacherie
Published 2021-09-15Version 1
For the Nonlinear Schrodinger equation in dimension 2, the existence of a global minimizer of the energy at fixed momentum has been established by Bethuel-Gravejat-Saut. This minimizer is a travelling wave for the Nonlinear Schrodinger equation. For large momentums, the propagation speed is small and the minimizer behaves like two well separated vortices. In that limit, we show the uniqueness of this minimizer, up to the invariances of the problem, hence proving the orbital stability of this travelling wave. This work is a follow up to two previous papers, where we constructed and studied a particular travelling wave of the equation. We show a uniqueness result on this travelling wave in a class of functions that contains in particular all possible minimizers of the energy.
Rarefaction pulses for the Nonlinear Schrodinger Equation in the transonic limit
Collision of two solitons for $1d$ Nonlinear Schrodinger Equation with same mass
Solutions of the Nonlinear Schrodinger Equation with Prescribed Asymptotics at Infinity
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