  The observation of traveling breathers (TBs) with large-amplitude oscillatory
tails realizes an almost 50-year-old theoretical prediction (Kuznetsov 1975)
and generalizes the notion of a breather. Two strongly nonlinear TB families
are created in a core-annular flow by interacting a soliton and a nonlinear
periodic (cnoidal) carrier. Bright and dark TBs are observed to move faster or
slower, respectively, than the carrier while imparting a phase shift. Agreement
with model equations is achieved. Scattering of the TBs are observed to be
physically elastic. The observed TBs generalize to many continuum and discrete
systems.
