  In this note, we review stability properties in energy spaces of three
important nonlinear Schr\"odinger breathers: Peregrine, Kuznetsov-Ma, and
Akhmediev. More precisely, we show that these breathers are unstable according
to a standard definition of stability. Suitable Lyapunov functionals are
described, as well as their underlying spectral properties. As an immediate
consequence of the first variation of these functionals, we also present the
corresponding nonlinear ODEs fulfilled by these NLS breathers. The notion of
global stability for each breather above mentioned is finally discussed. Some
open questions are also briefly mentioned.
