The $L^{2}$ sequential convergence of a solution to the one dimensional, mass-critical NLS above the ground state

TL;DR

This paper extends previous results on the convergence of solutions to the one-dimensional mass-critical nonlinear Schrödinger equation, showing that all non-scattering solutions converge sequentially in the L^2 sense without symmetry constraints.

Contribution

It generalizes earlier weak convergence results to all non-scattering solutions in 1D without symmetry assumptions.

Findings

All non-scattering solutions exhibit L^2 sequential convergence.

The result applies to solutions without symmetry constraints.

It broadens the understanding of solution behavior in 1D mass-critical NLS.

Abstract

In this paper we generalize a weak sequential result of \cite{fan20182} to any non-scattering solutions in one dimension. No symmetry assumptions are required for the initial data.