A note on Berestycki-Cazenave's classical instability result for nonlinear Schr\"odinger equations

TL;DR

This paper provides a concise alternative proof of Berestycki and Cazenave's classical instability result for standing waves in certain nonlinear Schrödinger equations, emphasizing the blow-up behavior.

Contribution

It introduces a shorter, more streamlined proof of a well-known instability result for nonlinear Schrödinger equations.

Findings

Simplified proof of classical instability theorem

Confirmation of blow-up behavior for standing waves

Enhanced understanding of nonlinear Schrödinger dynamics

Abstract

In this note we give an alternative, shorter proof of the classical result of Berestycki and Cazenave on the instability by blow-up for the standing waves of some nonlinear Schr\"odinger equations.