  We construct a family of closed string solutions with kinks in a subspace of
AdS_5 x S^5 and study their properties. In certain limits these solutions
become folded pulsating strings, although in general they are made of multiple
pulsating rectangles. One unusual feature of these solutions is that their
monodromy matrices are trivial, leading to vanishing quasi-momenta. Exact
Backlund transformations of these solutions are found, again giving vanishing
higher conserved charges. We also consider the fluctuation modes around these
solutions as well as the semiclassical splitting of these strings.
