  The issue of a recurrence of the modulationally unstable water wave trains
within the framework of the fully nonlinear potential Euler equations is
addressed. It is examined, in particular, if a modulation which appears from
nowhere (i.e., is infinitesimal initially) and generates a rogue wave which
then disappears with no trace. If so, this wave solution would be a breather
solution of the primitive hydrodynamic equations. It is shown with the help of
the fully nonlinear numerical simulation that when a rogue wave occurs from a
uniform Stokes wave train, it excites other waves which have different lengths,
what prevents the complete recurrence and, eventually, results in a
quasi-periodic breathing of the wave envelope. Meanwhile the discovered effects
are rather small in magnitude, and the period of the modulation breathing may
be thousands of the dominant wave periods. Thus, the obtained solution may be
called a quasi-breather of the Euler equations.
