  Channel flow of an incompressible fluid at Reynolds numbers above 2400
possesses a number of different spatially localized solutions that approach
laminar flow far upstream and downstream. We use one such relative
time-periodic solution, which corresponds to a spatially localized version of a
Tollmien-Schlichting wave, to illustrate how the upstream and downstream
asymptotics can be computed analytically. In particular, we show that for these
spanwise uniform states the asymptotics predict the exponential localization
that has been observed for numerically computed solutions of several canonical
shear flows but never properly understood theoretically.
