  Parker Solar Probe (PSP) observations during its first encounter at 35.7
$R_\odot$ have shown the presence of magnetic field lines which are strongly
perturbed to the point that they produce local inversions of the radial
magnetic field, known as switchbacks. Their counterparts in the solar wind
velocity field are local enhancements in the radial speed, or jets, displaying
(in all components) the velocity-magnetic field correlation typical of large
amplitude Alfv\'en waves propagating away from the Sun. Switchbacks and radial
jets have previously been observed over a wide range of heliocentric distances
by Helios, WIND and Ulysses, although they were prevalent in significantly
faster streams than seen at PSP. Here we study via numerical MHD simulations
the evolution of such large amplitude Alfv\'enic fluctuations by including, in
agreement with observations, both a radial magnetic field inversion and an
initially constant total magnetic pressure. Despite the extremely large
excursion of magnetic and velocity fields, switchbacks are seen to persist for
up to hundreds of Alfv\'en crossing times before eventually decaying due to the
parametric decay instability. Our results suggest that such switchback/jet
configurations might indeed originate in the lower corona and survive out to
PSP distances, provided the background solar wind is sufficiently calm, in the
sense of not being pervaded by strong density fluctuations or other gradients,
such as stream or magnetic field shears, that might destabilize or destroy them
over shorter timescales.
